A Republican says he will be the first senator to object when Congress certifies US President-elect Joe Biden's election victory next week.
Missouri's Josh Hawley said he had election integrity concerns, despite a lack of evidence for widespread fraud.
A group of Republicans in the lower chamber of Congress, the House of Representatives, is also planning to contest the election results.
But the objections are not expected to change the outcome.
The US Electoral College - which confirms November's presidential election result by awarding points for each state won by the two White House rivals - earlier this month cemented Mr Biden's victory over Donald Trump by 306-232.
These votes must be affirmed by Congress on 6 January. Inauguration Day, when the new Democratic president and vice-president are sworn in, will be on 20 January.
Since losing the election, Mr Trump has repeatedly alleged systemic voting fraud without substantiation. The Republican president's legal efforts to overturn results have been rejected by the courts.
What did Hawley say?
Mr Hawley said he could not vote to certify the electoral results "without raising the fact that some states, particularly Pennsylvania, failed to follow their own state election laws".
"At the very least, Congress should investigate allegations of voter fraud and adopt measures to secure the integrity of our elections. But Congress has so far failed to act."
Mr Hawley - a first-term senator rumoured to have presidential ambitions - did not specify any electoral fraud that could have changed the final result.
Meanwhile, Walmart was forced to issue an apology after the company's account tweeted that Mr Hawley was being a "sore loser".
The retail giant deleted the tweet and said it had been mistakenly posted by a member of their social media team.
Mr Hawley tweeted back at the superstore chain: "Now that you've insulted 75 million Americans, will you at least apologize for using slave labor?"
So what will happen when Congress meets?
Electoral count objections that are endorsed by a member of the House and a member of the Senate must be considered by lawmakers in a two-hour debate, followed by a vote.
But for a state's electoral votes to be rejected, a majority in both chambers must uphold the objection. This scenario is seen as all but impossible since Democrats hold a majority in the House and some Republicans in the Senate have already said they will not contest the results.
But congressman Mo Brooks, an Alabama Republican, has promised to object in the House, meaning the debate-and-vote on 6 January is virtually guaranteed to happen.
What have other Republicans said?
Senate Republican leader Mitch McConnell has been urging his party members to avoid forcing lawmakers into a politically embarrassing loyalty test of either backing the president or the voters.
Mr McConnell told Republicans on a private call earlier this month that such a vote would be "terrible".
Another top Republican, John Thune, has also said such a vote would "go down like a shot dog".
He warned it would not make sense as the "ultimate outcome" was obvious.
How did the Biden camp react?
Biden spokeswoman Jen Psaki described Mr Hawley's move to reporters as "antics".
"The American people spoke resoundingly in this election and 81 million people have voted for Joe Biden and Kamala Harris," she said.
"Congress will certify the results of the election as they do every four years."