The Biden administration has decided to allow Ukraine to strike inside Russia with U.S.-made weapons with the aim of blunting Russia’s attacks in the Kharkiv area, senior American officials said on Thursday.

The decision follows weeks of discussion with the Ukrainians after Russia began a major assault on Kharkiv, the second-largest city in Ukraine.

Because Kharkiv is near Russia, in the northeast of Ukraine, the Russian military has been hitting the area around the city with artillery and missiles fired or launched from inside Russian territory, and the Ukrainians have asked the Americans to give them greater leeway in defending Kharkiv, an American official said.

The permission from President Biden is intended solely for Ukraine to attack military sites in Russia being used to attack the Kharkiv area, U.S. officials said.

On Wednesday, Secretary of State Antony J. Blinken told reporters traveling with him in Moldova that the United States would “adapt and adjust” to battlefield conditions. He was responding to a question about whether Mr. Biden would soon allow Ukraine to use American-made weapons to strike in Russia. It was a strong suggestion that the president was making the decision to give permission to Ukraine.

The leaders of NATO, France and Germany had recently urged the United States to make that decision. In internal administration discussions, Mr. Blinken has advocated moving in that direction. He is attending a NATO meeting in Prague on Thursday and Friday and visited Ukraine more than two weeks ago.

The decision by Mr. Biden was reported earlier on Thursday by Politico.