President Biden has for the first time authorized the use of American long-range missiles by Ukraine to strike inside Russia. The decision is a major American policy shift and comes as Mr. Biden is about to leave office and incoming President-elect Trump has said he would bring about a swift end to the war and has expressed skepticism over continued support by the United States.

The weapons are likely to be used in response to North Korea’s decision to send thousands of troops to Russia in support of President Putin’s invasion of Ukraine.

The Ukrainian president, Volodymyr Zelenskyy, and many of his Western supporters have been pressing Mr. Biden for months to allow Ukraine to strike military targets inside Russia with Western-supplied missiles, saying the American ban had made it impossible for Ukraine to try to stop Russian attacks on its cities and electrical grids.

Some supporters have argued that this and other American constraints could cost Ukraine the war. The debate has become a source of disagreement among Ukraine’s NATO allies.

Mr. Biden had remained opposed, determined to hold the line against any escalation that he felt could draw the United States and other NATO members into direct conflict with Russia.

But North Korea has deployed thousands of troops to Russia to help Moscow try to claw back land in the Kursk border region that Ukraine seized this year. The introduction of North Korean troops to the conflict comes as Moscow has seen a favorable shift in momentum. Trump has signaled that he could push Ukraine to agree to give up some land seized by Russia to find an end to the conflict.

As many as 12,000 North Korean troops have been sent to Russia, according to American, South Korean and Ukrainian assessments. American and South Korean intelligence officials say North Korea also has provided Russia with significant amounts of munitions to replenish its dwindling weapons stockpiles.

Trump, who takes office in January, spoke for months as a candidate about wanting Russia’s war in Ukraine to be over, but he mostly ducked questions about whether he wanted Ukraine to win. He also repeatedly slammed the Biden administration for giving Kyiv tens of billions of dollars in aid. His election victory has Ukraine’s international backers worrying that any rushed settlement would mostly benefit Russia.

Mr. Putin has warned in the past that authorizing the use of long-range weapons against Russian targets would be tantamount to the United States going to war against Russia.