WASHINGTON — The director of the C.I.A. said on Thursday that Russian President Vladimir V. Putin’s “potential desperation” to extract the semblance of a victory in Ukraine could tempt him to order the use of a tactical or low-yield nuclear weapon, publicly discussing for the first time a concern that has coursed through the White House during seven weeks of conflict.

The director, William J. Burns, who served as American ambassador to Russia and is the member of the administration who has dealt most often with Mr. Putin, said the potential detonation of such a weapon — even as a warning shot — was a possibility that the United States remained “very concerned” about. But he quickly cautioned that so far, despite Mr. Putin’s frequent invocation of nuclear threats, he had seen no “practical evidence” of the kinds of military deployments or movement of weapons that would suggest such a move was imminent.

“Given the potential desperation of President Putin and the Russian leadership, given the setbacks that they’ve faced so far, militarily, none of us can take lightly the threat posed by a potential resort to tactical nuclear weapons or low-yield nuclear weapons,” Mr. Burns said during a question-and-answer session following a speech he delivered at the Georgia Institute of Technology.

He spoke in response to a question from former Senator Sam Nunn, of Georgia, who helped create the program that brought nuclear weapons out of Ukraine and other former Soviet states 30 years ago.

Tactical weapons are sometimes called “battlefield nukes,” smaller weapons that can be shot out of a mortar or even exploded like a mine, as opposed to “strategic” weapons that are put on intercontinental ballistic missiles. Russia has a large arsenal of tactical weapons; the United States keeps comparatively few. Low-yield nuclear weapons have been designed to produce a fairly small explosion, which sometimes blurs the difference between conventional and nuclear weapons.

Mr. Burns also argued that the disclosure of Mr. Putin’s intentions by U.S. intelligence officials before the outbreak of the war had made it harder for Mr. Putin to hide the “raw brutality” his forces have used in Ukraine, reminiscent of the damage Russian forces inflicted in Chechnya in the 1990s.

“I have watched over the years as Putin has stewed in a combustible combination of grievance and ambition and insecurity,” Mr. Burns said. He said the Russian president has nursed grievances against the West for decades, convinced the United States took advantage of Russia’s weakness after the breakup of the Soviet Union.

President Biden and his national security adviser, Jake Sullivan, both acknowledged Thursday that the White House was debating sending a high-level official to Kyiv, the capital of Ukraine, in a show of support for the government of President Volodymyr Zelensky. Prime Minister Boris Johnson of Britain recently took a secret trip to Kyiv by train.

Mr. Sullivan said that the White House had briefly considered having Mr. Biden go into Ukraine, but as soon as it became clear “what kind of footprint that would require, what kind of assets that would take from the Ukrainians as well as the U.S.” to keep him safe, the idea was rejected.

When pressed on reports that he, Secretary of State Antony J. Blinken or Defense Secretary Lloyd J. Austin III might go to Kyiv, Mr. Sullivan declined to discuss it, saying that “if and when that happens, we want to make sure it’s done in a very secure way.” Mr. Biden told reporters no decision had been made to send an envoy.

Mr. Sullivan also said that in coming days the United States would announce a crackdown on countries and companies violating the Western sanctions on Moscow, imposed since the invasion began in late February.

The Commerce Department on Thursday identified 10 aircraft that were flying into or operated by Belarus, with the apparent intention of registering them in Russia. The sanctions would prevent servicing or fueling the aircraft internationally, effectively grounding them.

Mr. Sullivan had made a similar vow to crack down on violators just ahead of Mr. Biden’s trip to Brussels and Warsaw last month. But on Thursday, speaking at the Economic Club of Washington, he said he believed that some of the sanctions — particularly export controls on defense technology — were beginning to hurt Russia’s military readiness.

“Russia’s ability to retool and replenish,” he said, was being set back because many of its systems “rely on Western microchips and components.”

“They are exhausting the stock of some of the high-end weapons,” Mr. Sullivan added, though he acknowledged that the continuing purchase of natural gas from Russia was helping to fund the war.

“I’m not sitting here suggesting we have so starved them of those resources they literally can’t field an army and continue to try to make progress on the battlefield,” Mr. Sullivan said. But he said Washington was stepping up the effort to help Europe wean itself off Russian gas by delivering supplies of liquefied natural gas from the United States.

But Mr. Sullivan also indicated that so far he had seen no evidence that China was stepping in to help Mr. Putin with either military or financial aid. His statement was notable because Mr. Biden, in a call with President Xi Jinping of China four weeks ago, had warned about American penalties should China aid the war effort. But the evidence since then has suggested that despite Mr. Putin and Mr. Xi’s declaration in February that their relationship has “no limits,” China in fact appears to be of mixed views on how much to support the war.

Mr. Burns and Mr. Sullivan both acknowledged that the war was moving to a new phase now that Russia appears to have narrowed its objective to taking the Donbas region in eastern Ukraine, where pro-Russia separatists have been fighting since 2014.

Gen. Philip Breedlove, the former supreme allied commander in Europe, who is now retired, said Thursday that while Mr. Putin may be able to paint his narrower operation as a win, the war will be a loss for Russia in the long term.

“Ukraine is still going to try to fight what I call the American Revolutionary War again, skirmishing and counterattacking and ambushing,” General Breedlove said. “It is just going to be a lot harder for them.”

By moving his forces to the east, Mr. Putin is looking to move the war to more favorable territory, trying to make it more difficult for the Ukrainian forces to stick with those tactics. “They are now prepared to fight the war that they really want,” General Breedlove said. “They want to meet force on force in open fields.”