WASHINGTON — Senator Mitch McConnell blocked an attempt by Democrats on Tuesday to hold an immediate vote on increasing stimulus checks to $2,000 from $600, leaving the fate of the measure unclear as President Trump continued to demand the larger payouts and more Republicans publicly endorsed the idea.

a person in a suit standing in front of a building: Senator Mitch McConnell’s decision to sidestep a vote came as a growing number of Republican senators came out in support of larger stimulus checks.© Al Drago for The New York Times Senator Mitch McConnell’s decision to sidestep a vote came as a growing number of Republican senators came out in support of larger stimulus checks.Instead, Mr. McConnell, Republican of Kentucky and the majority leader, provided vague assurances that the Senate would “begin the process” of discussing $2,000 checks and two other issues that Mr. Trump has demanded lawmakers address: election security and removing legal protections for social media platforms.

Mr. McConnell would not say whether he planned separate votes on the three issues or if he would bring them for a vote on the Senate floor at all. But in a sign of how he might approach them, the majority leader introduced new legislation on Tuesday afternoon combining the $2,000 checks, election security and social media provisions into one bill, which would most likely doom the effort.

The sudden talk of election security complicates matters, given that Mr. Trump continues to claim, without evidence, that voter fraud cost him re-election. Democrats would undoubtedly resist anything that could be seen as trying to undermine the outcome of the election.

Mr. McConnell, who has privately urged his conference members not to object to the election results when Congress meets on Jan. 6 to ratify them, portrayed the president’s request as “exploring further ways to protect the sanctity of American ballots.” The bill that Mr. McConnell is putting together would create a bipartisan commission to study election practices that “strengthened” and that “undermined the integrity of the election,” like the use of mail-in ballots and vote-by-mail procedures, which Mr. Trump has baselessly complained encouraged voter fraud.

a person standing in front of a mirror posing for the camera: Senator Chuck Schumer of New York, the Democratic leader, tried to force an immediate vote by using a procedural tactic but was blocked by Mr. McConnell.© Al Drago for The New York Times Senator Chuck Schumer of New York, the Democratic leader, tried to force an immediate vote by using a procedural tactic but was blocked by Mr. McConnell.Mr. McConnell’s move came as he faced growing pressure from Republicans to increase stimulus payments to struggling Americans.

Senators David Perdue and Kelly Loeffler of Georgia, who are facing tight runoff elections next week that will determine control of the Senate, announced on Tuesday that they supported increasing the size of individual stimulus checks to $2,000. They joined a handful of other Republican senators — including Marco Rubio of Florida, Josh Hawley of Missouri and Lindsey Graham of South Carolina — in calling for such action.

There are five days left in the current legislative session for the Senate to act. The lack of immediate action by the chamber rankled Mr. Trump, who lashed out at lawmakers in his own party.

“Unless Republicans have a death wish, and it is also the right thing to do, they must approve the $2000 payments ASAP,” Mr. Trump wrote on Twitter. “$600 IS NOT ENOUGH!”

The vast majority of Senate Republicans have long resisted the idea of larger stimulus checks, pointing to concerns about their cost and effectiveness. But that position was undercut after Mr. Trump held a $900 billion stimulus package and government spending bill hostage for days, insisting that lawmakers more than triple the direct payments to $2,000 from $600.

The president relented only after Republican lawmakers persuaded him to sign the legislation on Sunday. He said that he had been assured Congress would take up his demands for bigger checks, along with removing a legal shield for tech companies and investigating “very substantial voter fraud.” His claims that the election was stolen have been repeatedly contradicted by state election officials and judges across the nation.

The House voted on Monday evening to increase the size of the stimulus checks to $2,000, daring Senate Republicans to either approve the heftier sum or defy Mr. Trump.

But on Tuesday, Mr. McConnell thwarted an effort by Senator Chuck Schumer of New York, the Democratic leader, to force an immediate vote on bigger checks by using a procedural tactic that allows senators to advance legislation unless another senator objects.

“Senate Democrats strongly support $2,000 checks. Even President Trump supports $2,000 checks,” Mr. Schumer said. “There’s one question left today: Do Senate Republicans join with the rest of America in supporting $2,000 checks?”

Democrats, who have long called for increased direct payments, have sought to use the issue as a political cudgel in the Georgia runoff. Jon Ossoff and the Rev. Raphael Warnock, who are running against Ms. Loeffler and Mr. Perdue, have both called for higher stimulus checks, criticizing the $600 as insufficient and rebuking their opponents for not agitating to put more money in Georgians’ pockets.

On Tuesday, Mr. Perdue called increasing the checks “the right thing to do for people in Georgia,” and he said that he was “delighted to support the president.”

That amounted to a turnabout just one week before the election. In August, Mr. Perdue told “PBS NewsHour” that he was opposed to direct payments, arguing that tax incentives were a more effective means of relief. Ms. Loeffler had been largely silent on the issue, and told The Atlanta Journal-Constitution last week she would endorse the increase only if “it repurposes wasteful spending.”

Senator Bernie Sanders, independent of Vermont, moved on Tuesday to delay a planned vote on a military policy bill that Mr. Trump had vetoed, insisting that lawmakers first vote on the proposal to increase the size of stimulus checks to $2,000.

The delay could keep the Senate in Washington through New Year’s Day, a schedule that would be particularly burdensome to the Georgia senators, who are eager to stay on the campaign trail.

Other Republican senators have also begun to rally around bigger checks, which would go to individual adults with adjusted gross income on their 2019 tax returns of up to $75,000.

“Working Americans have borne the brunt of this pandemic,” Mr. Hawley wrote on Twitter. “They’ve been hammered, through no fault of their own. They deserve $2000 in #covid relief – a fraction of what the banks & big business got. Let’s vote now.”

And Senator Deb Fischer of Nebraska told reporters on Capitol Hill that her vote would depend on the legislation but said that “people are hurting and I think we need to get more aid.”

But the majority of Senate Republicans remain opposed to the plan.

“What we ought to be doing is focusing on the $900 billion that we’ve already approved and that Secretary Mnuchin helped us negotiate,” Senator John Cornyn of Texas said.

“Instead of taking appropriate credit for those good things, focusing on” the issue of larger checks, he continued, “undermines the very positive impact of what we’ve already done.”

“It’s such a huge number,” said Senator James M. Inhofe of Oklahoma. “I’d have a hard time supporting it.”

A decision by Mr. McConnell to link all of Mr. Trump’s demands together could sink the legislation. Democrats are unlikely to endorse a hasty overhaul of the legal shield currently in place for social media companies, known as Section 230 of the Communications Decency Act, especially measures put forward by Republican senators aimed at confronting what they believe is anticonservative bias.

Mr. Trump has attacked Section 230 for months, arguing without evidence that the law enables websites to censor conservative views. Data shows that conservative personalities and publishers often thrive online. Conservative Republicans have introduced multiple bills tackling the issue in the past two years, although none of them have become law.

While the concerns about Section 230 are bipartisan, it is unlikely that lawmakers could reach an agreement on the issue within the next week. Mr. Trump and his allies have yet to find substantial common ground with Democrats, who primarily want changes addressing discriminatory advertising or terrorist content online.

“If Senator McConnell tries loading up the bipartisan House-passed CASH Act with unrelated, partisan provisions that will do absolutely nothing to help struggling families across the country, it will not pass the House and cannot become law,” Mr. Schumer said in a statement. “Any move like this by Sen. McConnell would be a blatant attempt to deprive Americans of a $2,000 survival check.”

Despite the lack of action on a bigger check, the Treasury secretary, Steven Mnuchin, said in a tweet on Tuesday that the $600 checks could begin arriving in bank accounts as early as Tuesday evening and would continue into next week, while paper checks will start being mailed on Wednesday.

Source: McConnell blocks Senate vote on raising stimulus check amount to $2,000