Russia sought to turn the tables by accusing Ukraine and its allies of being the ones to widen the war, citing the supposed secret Polish-American plan to control western Ukraine and the recent attacks on targets inside Russia. Maria Zakharova, the Russian Foreign Ministry’s spokeswoman, urged Kyiv and Western capitals to take seriously Russia’s statements “that further calls on Ukraine to strike Russian facilities would definitely lead to a tough response from Russia.”

Mykhailo Podolyak, an adviser to Mr. Zelensky, said Ukraine had a right to strike Russian military facilities and “will defend itself in any way.” Britain’s defense minister, Ben Wallace, also said Ukraine would be justified in using Western arms to attack military targets inside Russia, as he warned that the war could turn into a “slow-moving, frozen occupation, like a sort of cancerous growth in Ukraine.”

Speaking at the White House, Mr. Biden rejected Russian suggestions that the United States was waging a proxy war against Moscow. “It shows the desperation that Russia is feeling about their abject failure in being able to do what they set out to do in the first instance,” Mr. Biden said.

He likewise condemned Russian officials’ raising the specter of nuclear war. “No one should be making idle comments about the use of nuclear weapons or the possibility that they could use that,” Mr. Biden said. “It’s irresponsible.”

The massive aid package Mr. Biden unveiled on Thursday would eclipse all the spending by the United States so far on the war. There is widespread bipartisan support on Capitol Hill for more aid, but it remained uncertain whether the issue could get tied up in negotiations over ancillary issues like pandemic relief or immigration.

The request, more than twice the size of the $13.6 billion package lawmakers approved and Mr. Biden signed last month, was intended to last through the end of September, underscoring the expectations of a prolonged conflict.

It includes more than $20 billion for security and military assistance, including $11.4 billion to fund equipment and replenish stocks already provided to Ukraine, $2.6 billion to support the deployment of American troops and equipment to the region to safeguard NATO allies and $1.9 billion for cybersecurity and intelligence support.