Ballistic missiles in Belarus, and to the east inside Russian territory, have captured British and Ukrainian attention in recent days. The Iskander-M missiles are mounted on mobile launchers, meaning they can be rolled closer to the border in short order, and they have a range of about 300 miles. That suggests that Mr. Putin, if he chose, could begin attacking cities and military emplacements before he moved any troops over the border.

Mr. Austin and General Milley described to lawmakers a bristling array of additional Russian military assets that have encircled Ukraine. They include 11 amphibious assault ships, in the Black Sea and in the Mediterranean, with the capacity to carry five battalions of Russian Marines who could land in Ukraine from the south, the officials said. In addition, Mr. Putin has deployed a number of submarines to the Black Sea, the defense officials told lawmakers.

Mr. Putin has also deployed Special Operations forces — some 1,500 troops — near and even inside the Ukrainian border, the officials told lawmakers. Those troops, they said, work closely with the Russian military intelligence agency, the G.R.U., which has in the past directed cyber- and other attacks on foes.

European officials tend to be more skeptical that Mr. Putin would try to take the country in a large-scale invasion. Some believe that he would seek to take the Donbas region of eastern Ukraine, where a grinding proxy war has been underway since 2014.

Another theory is that Mr. Putin could expand that operation in an effort to annex all of eastern Ukraine, up to the Dnieper River. Along the way, he could try to decimate Ukrainian troops in that part of the country, roughly half of the Ukrainian military. That could incite panic in the western part of Ukraine — where resistance to Russia might be highest — and prompt people to flee the country. Over time, that could lead top government officials to flee or to try to rule from exile.

American and European officials have made clear that a physical attack over the borders of Ukraine would lead to enormous sanctions on Russia’s banks, trade restrictions on semiconductors and other high-tech items and the freezing of the accounts of Russian oligarchs and leaders. But there is far less unanimity, as President Biden himself has acknowledged, about how to respond to a “minor incursion.” Or even what a minor incursion might be.

European and American officials worry that Mr. Putin might try to stage a coup in Kyiv. Another possibility is a cyberattack devised by Russia that tries to bring down parts or all of Ukraine’s electric and communications infrastructure, similar to the 2015 and 2016 attacks on parts of the country’s electric grid.