But some of Mr. Biden’s aides are doubtful there is any diplomatic process they can offer Mr. Putin that would dissuade him from his fundamental goal of destabilizing President Volodymyr Zelensky’s pro-Western government in Ukraine. While the troop movements are easily visible on satellite images, Russia is already employing a familiar campaign of disinformation, cyberattacks and military intimidation to unseat the country’s leadership. The officials spoke on the condition of anonymity to discuss Tuesday’s call.

Mr. Burns was sent in part because he was the American ambassador to Moscow during Mr. Putin’s rise to power and is well known to Russian officials. But his warnings to the Russian leader, whom he reportedly spoke to by phone, appear to have been largely ignored, officials say.

A senior American official told reporters in a briefing on Monday that the official U.S. assessment is still that Mr. Putin has not decided whether to conduct a full-scale invasion. But Mr. Putin and Mr. Biden, officials say, come to the conversation on Tuesday, which both men signaled they wanted, with very different agendas.

White House officials have been gaming out a series of scenarios with Mr. Biden, including that Mr. Putin has demands that go well beyond the familiar one that Ukraine can never join NATO. They include a reorientation of Ukraine away from the West and back into Moscow’s orbit.

Mr. Biden must convince Mr. Putin that the administration’s commitment to Ukraine, which it has called “unshakable,” is deep enough to cause tremendous economic pain to Russia — even if, as both men know, American forces would not come directly to Ukraine’s aid. Under discussion are steps as extreme as cutting off Russia’s access to the international financial settlement system, called SWIFT, and a series of restrictions on its banks like those honed in the effort to impose sanctions on Iran.

Russian forces are already deployed in the northeast, the south and the west, suggesting that Mr. Putin is putting together all the elements of a combined ground, cyber and information warfare campaign. The moves have prompted emergency meetings from Brussels to Washington — which may have been precisely what Mr. Putin intended.

At the Pentagon on Monday, Defense Secretary Lloyd J. Austin III convened top military and civilian officials, including Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, and Gen. Tod D. Wolters, the head of the military’s European Command, to discuss the Russian troop buildup. Officials said that there was an effort underway to send additional defensive weapons, including anti-tank Javelins, to Ukraine, but that they may be pre-positioned outside the country to avoid giving Mr. Putin a pretext for military action.