The Russian Defence Ministry denied being behind “any strikes on targets near the Ukrainian-Polish border” and said in a statement that photos of purported damage “have nothing to do” with Russian weapons.
A Nato official, speaking on condition of anonymity, said the alliance was looking into reports of a strike in Poland.
The US National Security Council said it was also looking into the reports.
Polish government spokesman Piotr Mueller did not immediately confirm the information from the US intelligence official, who spoke on condition of anonymity because of the sensitive nature of the situation.
But Mr Mueller said top leaders were holding an emergency meeting due to a “crisis situation”.
Polish media reported that two people died on Tuesday afternoon after a projectile struck an area where grain was drying in Przewodow, a Polish village near the border with Ukraine.
Neighbouring Moldova was also affected. It reported massive power outages after air strikes knocked out a key power line that supplies the small nation, an official said.
It comes amid a barrage of Russian airstrikes targeting energy facilities, causing power blackouts.
A senior official warned that the situation was “critical” and urged Ukrainians to “hang in there” as neighbourhoods went dark.
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 in the nearly nine-month war — the retaking last week of the southern city of Kherson.
At least a dozen regions reported strikes, which caused multiple emergency blackouts.
A Ukrainian air force spokesman said Russia fired around 100 missiles. President Volodymyr Zelensky put the number at 85.
Mr Zelensky warned that more attacks may be coming but defiantly vowed, with a shake of his fist: “We will survive everything.”
A senior official, Kyrylo Tymoshenko, said the barrage was “another planned attack on energy infrastructure facilities”.
“Most of the hits were recorded in the centre and in the north of the country. In the capital, the situation is very difficult,” Mr Tymoshenko wrote on Telegram.
As its battlefield losses mount, Russia has in recent months 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.
While city after city reported attacks, Mr Tymoshenko appealed to Ukrainians to hang on and acknowledged the severity of the situation.
Among regions where officials reported strikes were Lviv, Zhytomyr, Khmelnytskyi and Rivne in the west, and Kharkiv, Ukraine’s second largest city in the north east.
Several missile strikes also hit Kryvyi Rih, Zelenskyy’s native city, according to its mayor, Oleksandr Vilkul.
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. Mr Klitschko said air defence units also shot down some missiles.
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 its surrounds.
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, Ms Bogner said her teams are looking to travel to Kherson to try to verify allegations of nearly 80 cases of enforced disappearances and arbitrary detention it has turned up in the area and “understand whether the scale is in fact larger than what we have documented already”.
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”.
“Mine clearance is currently under way. After that, I think, today, investigative actions will begin,” he said on Ukrainian TV.
The retaking of Kherson was one of Ukraine’s biggest successes in the nearly nine-month-old Russian invasion and dealt another stinging blow to the Kremlin.
But large parts of eastern and southern Ukraine remain under Russian control and fighting continues.
Mr Zelensky on Tuesday likened the recapture of the Kherson to the Allied landings in France on D-Day in the Second World War, saying both were watersheds on the road to eventual victory.