For many months, President Biden has been rallying global leaders to provide more military aid to Ukraine and pressing Congress to pass a multibillion-dollar aid package to help the country beat back Russian aggression. Former President Donald J. Trump has been undermining that effort, pressing Republicans to thwart it.

But on Wednesday, Mr. Trump tried to flip the script, suggesting that he would do more to protect Ukraine than Mr. Biden, who he said would effectively cede Ukraine as a gift to President Vladimir V. Putin of Russia.

Speaking at a campaign event in North Charleston, S.C., Mr. Trump said that, under a Biden presidency, Mr. Putin is “going to be given everything he wants, including Ukraine. That’s a gift. He’s got a gift.”

Then Mr. Trump — who often positively invokes Mr. Putin as an authoritarian strongman, and who acknowledged in his speech that they got along — doubled down, saying that Mr. Biden “is going to give” Ukraine to Mr. Putin.

Mr. Biden has repeatedly vowed to help Ukraine defend itself for “as long as it takes,” pledging that “our commitment to Ukraine will not weaken.” Mr. Trump, by contrast, has previously said that he would consider letting Russia “take over” parts of Ukraine in a negotiated deal to end the war.

A day earlier, the Senate, in a bipartisan vote, approved an additional $60.1 billion in assistance to Kyiv to help it fight Russia’s invasion, part of a long-debated foreign aid package for Ukraine and Israel.

After the Senate vote, Mr. Biden accused Mr. Trump of bowing down to Russia. Mr. Biden has previously argued that aid for Ukraine is necessary to keep Mr. Putin from gaining ground in the war, and that a failure to provide assistance could ultimately encourage Mr. Putin to attack NATO allies, which could draw the United States into direct conflict with Russia.

But that effort faces significant resistance from Republicans in the House, many of whom have been encouraged by Mr. Trump’s “America First” views on foreign policy and his criticisms of the legislation on the campaign trail.

Earlier this week on social media, Mr. Trump said it was “stupid” for the United States to offer foreign aid to countries instead of loans. And he has repeatedly been critical of the United States’ involvement in the war in Ukraine, arguing that Europeans who are worried about Russian aggression should be spending more to fight it.

Mr. Trump often posits that the mere fact of his presidency, had he won in 2020, would have been enough to keep Russia at bay. In his stump speech, he routinely promises that he will settle the war quickly if he is elected, and he has often said that he could resolve the conflict “within 24 hours.”

But European leaders and security experts have expressed concerns that a second Trump presidency could embolden Russia, particularly given Mr. Trump’s frequent threats to withdraw the United States from NATO.

Further feeding their fears, Mr. Trump on Saturday raised the possibility that he might “encourage” Russia “to do whatever the hell they want” against NATO members that were not spending enough money on their own defense. His comments spurred a firestorm of criticism from Mr. Biden and Nikki Haley, his lone major rival in the Republican primary.

After days of headlines, Mr. Trump did not restate that claim on Wednesday. But he returned to his more frequent contention that he had told NATO members that the United States would not defend them if he deemed their spending insufficient.

NATO has a nonbinding goal that its member countries spend 2 percent of their gross domestic product on their militaries. As of last year, just 11 of 31 NATO members had reached that level. Mr. Trump on Wednesday said he thought the goal should be doubled to 4 percent.