The war launched by Russian President Vladimir Putin ground into its fourth week as his troops have failed to take Kyiv, a major objective in their hopes of forcing a settlement or dictating the country's future political alignments.

Missiles and shelling struck the edges of Kyiv as well as Lviv, close to Ukraine's western border with NATO countries such as Poland.

Late Thursday, Ukrainian President Volodymyr Zelenskyy said in his nighttime video address to the nation that he is thankful to U.S. President Joe Biden for additional military aid but won't say specifically what the new package includes because he doesn't want to tip off Russia.

Foreign ministers of the Group of Seven leading economies meanwhile said in a joint statement that Russian President Vladimir Putin is conducting an "unprovoked and shameful war.''

The fighting has led more than 3 million people to flee Ukraine, the U.N. estimates. The death toll remains unknown, though Ukraine has said thousands of civilians have died.

Here are some key things to know about the conflict:

WHAT IS HAPPENING ON THE GROUND?

The Ukrainian air force's western command said that six missiles were launched at Lviv from the Black Sea, but that two of them were shot down.

The city's mayor, Andriy Sadovyi, said the missiles hit a facility for repairing military aircraft near Lviv's international airport, also damaging a bus repair facility. No casualties were immediately reported. The facility had suspended work ahead of the attack, the mayor said on the Telegram messaging app.

Early morning barrages also hit a residential building in the Podil neighbourhood of Kyiv, killing at least one person, according to emergency services, who said 98 people were evacuated from the building. Kyiv mayor Vitali Klitschko said 19 were wounded in the shelling, just north of downtown Kyiv.

Two other people were killed when strikes hit residential and administrative buildings in the eastern city of Kramatorsk, according to the regional governor, Pavlo Kyrylenko.

Civilian casualties have been mounting. The United Nations says that so far it has recorded 780 killed and 1,252 injured, although it estimates actual casualties are much higher. It says that most of the civilian casualties were due to explosive weapons with a wide impact area, such as heavy artillery and multiple-launch rocket systems as well as missile and airstrikes.

Ukrainian officials say thousands of civilians have been killed.

The World Health Organization has verified 43 attacks on hospitals and health facilities, with 12 people killed and 34 injured, WHO Director-General Tedros Adhanom Ghebreyesus told the United Nations Security Council in a virtual briefing Thursday.

The besieged southern city of Mariupol has borne much of the bombardment. There, rescuers continue to search for survivors of a Russian airstrike on a theatre where hundreds of people were sheltering, local officials said.

With communications disrupted across the city and movement difficult because of shelling and another fighting, there were conflicting reports on whether anyone had emerged from the rubble.

Video and photos provided by the Ukrainian military showed that the building had been reduced to a roofless shell, with some exterior walls collapsed. Petro Andrushchenko, an official with the mayor's office, said the building had a relatively modern basement bomb shelter designed to withstand airstrikes.

Russia's military denied bombing the theatre or anyplace else in Mariupol on Wednesday.

Meanwhile, Britain's Defense Ministry said Thursday that Russia's invasion "has largely stalled on all fronts'' amid stiff Ukrainian resistance. It said Russian forces have made "minimal progress'' on land, sea or air in recent days, and are suffering heavy losses.

Ukrainian forces are using inexpensive Turkish-made drones to carry out lethal attacks on the Russian invaders.

WHAT HAS THE AP DIRECTLY WITNESSED OR CONFIRMED?

Smoke could be seen rising from the western part of the capital Kyiv after an early morning barrage Friday. Outside Lviv, black smoke billowed for hours after the early morning strike by several missiles,

A soldier standing guard near the site of the strike in Lviv said he heard three blasts in quick succession around 6 a.m. He said he had not heard of any casualties. A nearby resident described his building vibrating from the explosions and people panicking. Smoke continued to rise from the site almost three hours later.

The attacks in Mariupol knocked out the windows of apartment buildings and sent smoke rising above the skyline. Cars, some with the "Z'' symbol of the Russian invasion force in their windows, drove past stacks of ammunition boxes and artillery shells in a neighbourhood controlled by Russian-backed separatists.

In Kharkiv, doctors are struggling to treat COVID-19 patients as the bombs fall outside. Several times a day, air raid sirens wail at a local hospital, sending virus patients, some connected to ventilators and struggling to breathe, into bomb shelters.

HOW IS THE WORLD RESPONDING TO THE WAR?

Film icon Arnold Schwarzenegger told Russians in a video posted on social media Thursday they're being lied to about the war in Ukraine. He also accused Putin of sacrificing Russian soldiers' lives for his own ambitions.

Schwarzenegger posted his video on Twitter, YouTube and Instagram. While some of those services are blocked in Russia, he also posted it on the Telegram messaging app, which is not, where it got more than a half-million views. It was subtitled in Russian.

U.S. President Joe Biden and China's Xi Jinping are scheduled to speak by phone on Friday. Biden also plans to travel to Europe next week for talks with European leaders about the Russian invasion and will attend an extraordinary NATO summit in Brussels. NATO has been bolstering its eastern flank with troops and equipment to deter Russia from invading any of its members.

U.S. Secretary of State Antony Blinken said American officials are evaluating and documenting potential war crimes committed by Russia in Ukraine. Blinken said the intentional targeting of civilians is a war crime, for which there will be "massive consequences.''