Senate Minority Leader Mitch McConnell, R-Ky., left, speaks to Sen. Richard Shelby, R-Ala., as they attend a Senate Rules and Administration Committee meeting on the Electoral Count Reform and Presidential Transition Improvement Act, at the Capitol in Washington on Tuesday. J. Scott Applewhite/Associated Press

WASHINGTON — Senate Republican leader Mitch McConnell said Tuesday he will “proudly support” legislation to overhaul rules for certifying presidential elections, bolstering a bipartisan effort to revise a 19th-century law and avoid another Jan. 6 insurrection.

The legislation would clarify and expand parts of the 1887 Electoral Count Act, which, along with the Constitution, governs how states and Congress certify electors and declare presidential winners. The changes in the certification process are in response to unsuccessful efforts by former President Donald Trump and his allies to exploit loopholes in the law to overturn his 2020 defeat to Joe Biden.

“Congress’ process for counting the presidential electors’ votes was written 135 years ago,” McConnell said. “The chaos that came to a head on Jan. 6 of last year certainly underscored the need for an update.”

McConnell made the remarks just before the Senate Rules Committee voted 14-1 to approve the bill and send it to the Senate floor, where a vote is expected after the November election. The only senator to vote against the legislation was Republican Sen. Ted Cruz of Texas, one of two senators to stand and object to Biden’s certification last year.

The Republican leader’s endorsement gave the legislation a major boost as the bipartisan group pushes to pass the bill before the end of the year and ahead of the next election cycle. Trump is still pushing false claims of election fraud and saying he won the election as he considers another run in 2024.

Among the Republicans on the Rules panel who voted for the bill shortly after McConnell’s statement were Mississippi Sen. Cindy Hyde-Smith, one of only eight senators to vote against Biden’s certification, and Tennessee Sen. Bill Hagerty, a strong Trump ally.

The House has already passed a more expansive bill overhauling the electoral rules, but it has far less Republican support. While the House bill received a handful of Republican votes, the Senate version already has the backing of at least 12 Republicans — more than enough to break a filibuster and pass the legislation in the 50-50 Senate.

Senators made minor tweaks to the legislation at Tuesday’s meeting but kept the bill largely intact. The bill, written by Republican Sen. Susan Collins of Maine and Democratic Sen. Joe Manchin of West Virginia, would make clear that the vice president only has a ceremonial role in the certification process, tighten the rules around states sending their votes to Congress and make it harder for lawmakers to object.

Collins and Manchin issued a joint written statement after the committee vote.

“By moving our legislation through regular order, we were able to produce a strong package that has received broad, bipartisan support,” they said.  “We will keep working to increase support for our legislation that would correct the flaws in this archaic and ambiguous law.”

Sen. Angus King, I-Maine, has also supported the Senate efforts and praised the committee vote Tuesday in a written statement.

“While I continue to look for ways to better protect the democratic process for all Americans registered to vote before and on election day, this effort will better guarantee that the will of the voters cannot be undermined after votes are cast,” King said.

The changes are a direct response to Trump, who publicly pressured several states, members of Congress and then-Vice President Mike Pence to aid him as he tried to undo Biden’s win. Even though Trump’s effort failed, lawmakers in both parties said his attacks on the election showed the need for stronger safeguards in the law.

If it becomes law, the bill would be Congress’ strongest legislative response yet to the Jan. 6, 2021, attack, in which hundreds of Trump’s supporters beat police officers, broke into the Capitol and interrupted the joint session as lawmakers were counting the votes. Once the rioters were cleared, the House and Senate rejected GOP objections to the vote in two states. But more than 140 Republicans voted to sustain them.

Differences between the House and Senate bills will have to be resolved before final passage, including language around congressional objections.

While the Senate bill would require a fifth of both chambers to agree on an electoral objection to trigger a vote, the House bill would require agreement from at least a third of House members and a third of the Senate. Currently, only one member of each chamber is required for the House and Senate to vote on whether to reject a state’s electors.

The House bill also lays out new grounds for objections, while the Senate does not.

Associated Press writer Lisa Mascaro contributed to this report.