Both privately and publicly, Mr. McConnell has made the case that failing to stop President Vladimir V. Putin’s campaign in Ukraine would upend the international security order and pose a grave threat to the United States’ security. He made a similar argument in 2014, when he pressed for the United States to send aid to Kyiv as Mr. Putin invaded Crimea.

“This is not charity we’re involved in here,” he said on Sunday. “This is our interest — to help Ukrainians. Just like it is in the interest of NATO countries. This is not some handout. This is to prevent this ruthless thug from beginning a march through Europe.”

Behind closed doors, Mr. McConnell sought to bolster the Ukrainian government early in Russia’s invasion, his allies said, making the case himself and inviting top Ukrainian officials, including the ambassador to the United States, Oksana Markarova, to speak to his conference.

“His message very early was, ‘We need to get the Ukrainians anything they need, as quick as we can get it to them,’ ” said Senator Roy Blunt, Republican of Missouri.