A defiant Ukrainian President Volodymr Zelenskyy shook his fist and declared: "We will survive everything.''
Polish government spokesman Piotr Mueller did not immediately confirm the information from a senior US intelligence official, who spoke on condition of anonymity because of the sensitive nature of the situation.
But Mueller said top leaders were holding an emergency meeting due to a "crisis situation.''
Polish media reported that two people died Tuesday afternoon after a projectile struck an area where grain was drying in Przewodow, a Polish village near the border with Ukraine.
Neighboring Moldova was also affected. It reported massive power outages after the strikes knocked out a key power line that supplies the small nation, an official said.
Zelenskyy said Russia fired at least 85 missiles, "most of them at our energy infrastructure," and shut down power in many cities.
"We're working, will restore everything. We will survive everything," the president vowed. His energy minister said the attack was "the most massive'' bombardment of power facilities in the nearly 9-month-old Russian invasion, striking both power generation and transmission systems.
The minister, Herman Haluschenko, described the missile strikes as ``another attempt at terrorist revenge'' after military and diplomatic setbacks for the Kremlin. He accused Russia of "trying to cause maximum damage to our energy system on the eve of winter.''
The aerial assault, which resulted in at least one death in a residential building in the capital, Kyiv, followed days of euphoria in Ukraine sparked by one of its biggest military successes, the retaking last week of the southern city of Kherson.
The power grid was already battered by previous attacks that destroyed an estimated 40% of the country's energy infrastructure.
Russian President Vladimir Putin has not commented on the retreat from Kherson since his troops pulled out in the face of a Ukrainian offensive. But the stunning scale of Tuesday's strikes spoke volumes and hinted at anger in the Kremlin.
By striking targets in the late afternoon, not long before dusk began to fall, the Russian military forced rescue workers to labor in the dark and gave repair crews scant time to assess the damage by daylight.
More than a dozen regions, among them Lviv in the west, Kharkiv in the northeast and others in between, reported strikes or efforts by their air defenses to shoot missiles down.
At least a dozen regions reported power outages, affecting cities that together have millions of people. Almost half of the Kyiv region lost power, authorities said. Ukrainian Railways announced nationwide train delays.
Zelenskyy warned that more strikes were possible and urged people to stay safe and seek shelter.
"Most of the hits were recorded in the center and in the north of the country. In the capital, the situation is very difficult,'' said a senior official, Kyrylo Tymoshenko.
He said a total of 15 energy targets were damaged and claimed that 70 missiles were shot down. A Ukrainian Air Force spokesman said Russia used X-101 and X-555 cruise missiles.
As city after city reported attacks, Tymoshenko urged Ukrainians to "hang in there.''
With its battlefield losses mounting, Russia has increasingly resorted to targeting Ukraine's power grid, seemingly hoping to turn the approach of winter into a weapon by leaving people in the cold and dark.
In Kyiv, Mayor Vitali Klitschko said authorities found a body in one of three residential buildings that were struck in the capital, where emergency blackouts were also announced by power provider DTEK.
Video published by a presidential aide showed a five-story, apparently residential building in Kyiv on fire, with flames licking through apartments. Klitschko said air defense units also shot down some missiles.
Dutch Foreign Minister Wopke Hoekstra took to a bomb shelter in Kyiv after meeting his Ukrainian counterpart and, from his place of safety, described the bombardment as "an enormous motivation to keep standing shoulder-to-shoulder'' with Ukraine.
"There can be only one answer, and that is: Keep going. Keep supporting Ukraine, keep delivering weapons, keep working on accountability, keep working on humanitarian aid," he said.
Ukraine had seen a period of comparative calm since previous waves of drone and missile attacks several weeks ago.
The strikes came as authorities were already working furiously to get Kherson back on its feet and beginning to investigate alleged Russian abuses there and in the surrounding area.
The southern city is without power and water, and the head of the UN human rights office's monitoring mission in Ukraine, Matilda Bogner, on Tuesday decried a "dire humanitarian situation'' there.
Speaking from Kyiv, Bogner said her teams are looking to travel to Kherson to try to verify allegations of nearly 80 cases of forced disappearances and arbitrary detention.
The head of the National Police of Ukraine, Igor Klymenko, said authorities are to start investigating reports from Kherson residents that Russian forces set up at least three alleged torture sites in now-liberated parts of the wider Kherson region and that "our people may have been detained and tortured there.''
The retaking of Kherson dealt another stinging blow to the Kremlin. Zelenskyy likened the recapture to the Allied landings in France on D-Day in World War II, saying both were watershed events on the road to eventual victory.
But large parts of eastern and southern Ukraine remain under Russian control, and fighting continues.
Zelenskyy warned of possible more grim news ahead.
"Everywhere, when we liberate our land, we see one thing _ Russia leaves behind torture chambers and mass burials. . How many mass graves are there in the territory that still remains under the control of Russia?" Zelenskyy asked.