WASHINGTON — President Vladimir V. Putin of Russia has deployed the troops and military hardware needed to invade all of Ukraine, the Pentagon’s top leaders said on Friday, as senior Defense Department officials warned that the tense standoff was leading the United States, its NATO allies and Russia into uncharted territory.

Russia has assembled more than 100,000 troops at Ukraine’s borders, the officials said, publicly confirming for the first time what intelligence analysts have described for weeks. Those troops, Pentagon officials said, have the ability to move throughout Ukraine, far beyond an incursion into only the border regions.

Defense Secretary Lloyd J. Austin III described a bristling array of the Russian combined arms formations, artillery and rockets assembled at the Ukrainian border, which he said “far and away exceeds what we would typically see them do for exercises.”

Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, was more blunt: “I think you’d have to go back quite a while to the Cold War days to see something of this magnitude.”

Their comments came at a news conference at the Pentagon that was dominated by the unfolding crisis in Ukraine. Both men presented a grim picture of the situation, and Defense Department officials have privately warned that a Russian invasion has the potential to start a conflict between Moscow and the West that could quickly escalate.

U.S. officials estimate that 35,000 Americans are in Ukraine, including 7,000 people who have registered with the U.S. Embassy in Kyiv, the capital. While the State Department has advised Americans to leave the country and begun emptying out the embassy, Pentagon officials know well from their experience in Afghanistan over the summer that American citizens often do not heed advice.

Mr. Austin did not rule out the possibility that U.S. troops might be sent to Ukraine to evacuate Americans if Russia invades and there is combat in the streets of Kyiv. But that is exactly the type of situation that officials fear could lead to the escalation that Pentagon leaders want to avoid.

Mr. Austin has put 8,500 U.S. troops on high alert for possible deployment to Eastern Europe, where most of them would join a NATO rapid response team of 30,000 to 40,000 troops. And while President Biden has made clear that he has no intention of deploying U.S. troops to Ukraine to help fend off an invasion, he indicated this week that he might separately send additional troops to Eastern European allies that are worried about Russian advances.

Ukraine is not a member of NATO, so the United States has no treaty obligation to defend it. But the alliance’s so-called eastern flank — former Soviet satellites and the Baltic countries — are concerned that they could be next on Mr. Putin’s list.