Ukrainian President Volodymyr Zelenskyy's office, meanwhile, announced plans for a meeting Monday with a Russian delegation at an unspecified location on the Belarusian border.
Russia's military assault on Ukraine entered its fifth day with fighting in the streets of the country's second-largest city, Kharkiv, and troops moving closer to the capital, Kyiv.
Here are the things to know about the Russian invasion of Ukraine and the security crisis in Europe:
Russia Puts Nuclear Forces on Alert
Unearthing long-buried fears from the Cold War, Putin on Sunday ordered Russian nuclear weapons prepared for increased readiness to launch.
He said NATO had made ``aggressive statements'' toward Russia and cited the stiff economic sanctions imposed on Russia.
NATO Secretary-General Jens Stoltenberg told CNN that Putin's invocation of Russia's nuclear arsenal was ``dangerous rhetoric.''
The practical meaning of Putin's order was not immediately clear. Russia and the United States typically have land- and submarine-based nuclear forces on alert and prepared for combat at all times, but nuclear-capable bombers and other aircraft are not.
Fighting Spreads in Ukraine
Russian troops drew closer to Kyiv, a city of almost 3 million, and street fighting broke out in Kharkiv. Strategic ports in the south were coming under pressure from attackers.
Ukrainian defenders put up stiff resistance that appeared to slow the invasion. But a U.S. official cautioned that far stronger Russian forces inevitably will learn and adapt their tactics as Russia's assault goes on.
Only an occasional car appeared on a deserted main boulevard of Kyiv as a strict 39-hour curfew kept people off the streets until Monday morning. Authorities warned that anyone venturing out without a pass would be considered a Russian saboteur.
Terrified residents instead hunkered down in homes, underground garages and subway stations in anticipation of a full-scale Russian assault.
``I wish I had never lived to see this,'' said Faina Bystritska, 87, a Jewish survivor of World War II. She said sirens blare almost constantly in her hometown, Chernihiv, which is about about 150 kilometers (90 miles) from Kyiv and under attack.
Ukrainians have volunteered en masse to defend their country, taking guns distributed by authorities and preparing firebombs. Ukraine is also releasing prisoners with military experience who want to fight for the country, authorities said.
Pentagon officials said Russian troops are being slowed by Ukrainian resistance, fuel shortages and other logistical problems, and that Ukraine's air defense systems, while weakened, are still operating.
Russia and Ukraine to Hold Talks
After rejecting Putin's offer to meet in the Belarusian city of Homel on the grounds that Belarus was helping the Russian assault, Zelenskyy agreed to send a Ukrainian delegation to meet Russian counterparts at an unspecified time and location on the Belarusian border.
The announcement came hours after Russia announced that its delegation had flown to Belarus to await talks. Ukrainian officials initially rejected the move, saying any talks should take place elsewhere. Belarus has allowed Russia to use its territory as a staging ground for the invasion of Ukraine.
Zelenskyy named Warsaw, Bratislava, Istanbul, Budapest and Baku as alternative venues for talks, before accepting the Belarus border.
The Kremlin added later that Israeli Prime Minister Naftali Bennett had offered to help broker an end to the fighting in a call with Putin. It didn't say whether the Russian leader accepted.
Many Ukrainians Flee, Some Return to Fight
The number of Ukrainians fleeing Europe's largest armed conflict since World War II grew to 368,000, mostly women and children, the United Nations' refugee agency said Sunday. That figure more than doubles the agency's estimate from the day before.
The line of vehicles at the Poland-Ukraine border stretched for 14 kilometers (almost 9 miles), and those fleeing had to endure long waits in freezing temperatures overnight. Over 100,000 people have crossed into Poland alone, according to Polish officials. An additional 66,000 refugees have entered Hungary, with more than 23,000 entering on Saturday alone, according to the Hungarian officials.
In the rush to escape the bombs and tanks, a trickle of brave men and women headed home to defend Ukraine. At a border crossing in southern Poland, Associated Press journalists spoke to people in a line heading against the tide. They included 20 Ukrainian truck drivers who worked in Europe and wanted to face combat.
The World Moves to Punish Russia Further
Following punishing economic sanctions, the European Union agreed to close its airspace to Russia's airlines and spend hundreds of millions of euros on weapons to send to Ukraine as well as target pro-Kremlin media outlets that are spreading disinformation about the invasion.
European Commission President Ursula von der Leyen said the commission wants ``for the first time ever'' to finance the purchase and delivery of weapons to a third-party county under attack.
EU foreign policy chief Josep Borrell said the bloc's 27 foreign ministers on Sunday had greenlighted the unprecedented support for Ukraine and that those actions would take effect within hours.
Japan joined the U.S. and European nations in cutting top Russian banks off from the SWIFT international financial messaging system. Japan will also send $100 million in emergency humanitarian aid to Ukraine.
And petroleum giant BP said Sunday it is cutting ties with Rosneft, a state-owned Russian oil and gas company. That means BP exiting its stake in Rosneft and BP officials resigning positions on the Russian company's board.
Signs of Deeper Financial Difficulties in Russia
There were some early signs that the initial economic damage to the Russian economy is significant.
The ruble sank against the U.S. dollar early Monday after Western nations moved to block Russian banks from the SWIFT global payment system.
Videos from Russia showed long lines of Russians trying to withdraw cash from ATMs, while the Russian Central Bank issued a statement calling for calm, in an effort to avoid bank runs. Reports also said that Visa and Mastercard were no longer being accepted for those with international bank accounts.
Russia may have to close certain bank branches temporarily or declare a national bank holiday to protect its financial system, analysts said.
``If there's a full-scale banking panic, that's a driver of crisis in its own right,'' said Adam Tooze, a professor of history at Columbia University and Director of the European Institute. ``A rush into dollars by the Russian general population moves things into an entirely new domain of financial warfare.''
More Stingers Headed to Ukraine
The U.S. for the first time has approved the direct delivery of Stinger surface-to-air missiles to Ukraine. They can be used to shoot down helicopters and other aircraft. The decision was confirmed by U.S officials speaking on condition of anonymity.
The decision comes on the heels of Germany's announcement that it will send 500 Stinger missiles and other weapons and supplies to Ukraine.
The Baltic states have also been providing Ukraine with Stingers since January, and in order to do that had to get U.S. permission.
Germany also announced Saturday that it would send 1,000 anti-tank weapons, in addition to the 400 German-made anti-tank weapons it also approved to be shipped from the Netherlands.
The Stingers from the U.S. are part of an additional $350 million in military assistance to Ukraine, which also will include anti-tank weapons, body armor and small arms.
European countries will also supply fighter jets to Ukraine, Borrell said.
Two non-NATO members also were sending military supplies. Sweden said Sunday it would ship 5,000 anti-tank weapons, 5,000 helmets, 5,000 body armors and 135,000 field rations, while Finland said it would send 2,000 helmets, 2,000 bullet proof vests, 100 stretchers and equipment for two emergency medical care stations.
Russians against the War
Defying crackdowns by police, demonstrators marched in city centers from Moscow to Siberia chanting ``No to war!''
In St. Petersburg, where several hundred gathered in the city center, police in full riot gear were grabbing one protester after another and dragging some into police vans, even though the demonstration was peaceful. Footage from Moscow showed police throwing several female protesters on the ground before dragging them away.
According to the OVD-Info rights group, which tracks political arrests, by Sunday evening police detained at least 1,474 Russians in 45 cities over antiwar demonstrations that day, bringing the total detained in the last few days to over 5,000.
``I have two sons and I don't want to give them to that bloody monster,`` Dmitry Maltsev, 48, who joined the rally in St. Petersburg, told The Associated Press. ``War is a tragedy for all of us.''
Protests also took place in Belarus, where more than 500 people were detained on Sunday, according to the country's most prominent human rights group. The Viasna human rights center said demonstrations were held in at least 12 cities, including Minsk, the capital. Demonstrators placed flowers on a growing pile outside the Ukrainian Embassy.
Russia Acknowledges Casualties
The Russian military acknowledged that it has suffered casualties in Ukraine, without putting a number on them. ``There are dead and wounded among our comrades,'' said Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov.
Each side in the war has made claims about casualties and military damage inflicted on the other side, but the numbers have not been verified. Konashenkov's statement was the first by Russian military officials to admit any troop losses of their own.
Ukraine acknowledged military casualties early on. It has not given a number. Ukraine reports civilian deaths and said Sunday that 352 people have been killed, including 14 children.
United Nations to Meet
The U.N.'s two major bodies, the 193-nation General Assembly and the more powerful 15-member Security Council, are holding separate meetings Monday on Russia's invasion of Ukraine.
The Security Council gave a green light Sunday for the first emergency session of the General Assembly in decades. It will give all U.N. members an opportunity to speak about the war Monday and vote on a resolution later in the week that U.S. Ambassador Linda Thomas-Greenfield said would ``hold Russia to account for its indefensible actions and for its violations of the U.N. Charter.''