In the past three days, the American secretary of defense has called for an effort to degrade the capability of the Russian military so that it could not invade another country for years to come. The Russians have cut off gas shipments to Poland and Bulgaria, which joined the North Atlantic Treaty Organization after the collapse of the Soviet Union; Ursula von der Leyen, the president of the European Commission, immediately denounced the move as an “instrument of blackmail.” Explosions have rocked a disputed area of Moldova, a natural next target for the Russians, and gas depots and even a missile factory in Russia have mysteriously caught fire or come under direct attack from Ukrainian forces.

And with increasing frequency, the Russians are reminding the world of the size and power of their nuclear arsenal, an unsubtle warning that if President Vladimir V. Putin’s conventional forces face any more humiliating losses, he has other options. American and European officials say they see no evidence the Russians are mobilizing their battlefield nuclear forces, but behind the scenes, the officials are already gaming out how they might react to a Russian nuclear test, or demonstration explosion, over the Black Sea or on Ukrainian territory…

“Putin is not willing to back down, nor are the Ukrainians, so there is more blood to come,” said Robin Niblett, the director of Chatham House, a British think tank. At the same time, American and European determination to help Ukraine defeat the Russians has hardened, partly after the atrocities in Bucha and other towns occupied by the Russians became clear, with even Germany overcoming its initial objections and sending artillery and armored vehicles.