The Senate Republican leader, Mitch McConnell, said on Tuesday he would “proudly support” legislation to overhaul rules for certifying presidential elections, bolstering a bipartisan effort to revise a 19th-century law and avoid any repeat of the January 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 Donald Trump and his allies to exploit loopholes in the law and overturn his 2020 defeat by Joe Biden.

McConnell made the remarks just before a committee vote on the legislation. He said he would back the bill as long as a bipartisan agreement on the language was not significantly changed.

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

McConnell noted that in addition to Republican objections to Biden’s win, Democrats objected the last three times that Republicans won presidential elections. The legislation would make it harder for Congress to sustain those objections.

A total of 147 Republicans in the House and Senate objected to results in key states won by Biden. Handfuls of Democrats objected to Donald Trump’s victory in 2016 and George W Bush’s wins in 2000 and 2004.

McConnell’s comments gave the legislation a major boost as its bipartisan sponsors push to pass the bill before the end of the year and the next election cycle. Trump is still lying about election fraud as he considers another run.

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

The Senate rules committee was expected to approve the legislation on Tuesday and send it to the full chamber. A vote isn’t expected until after the November elections.

Senators were expected to make minor tweaks to the legislation but keep the bill largely intact. The bill, written by the Republican Susan Collins of Maine and Joe Manchin of West Virginia, a Democrat, would make clear that the vice-president only has a ceremonial role in the certification process, tighten the rules on states sending votes to Congress and make it harder for lawmakers to object.

Trump publicly pressured states, members of Congress and his vice-president, Mike Pence, to undo Biden’s win. Even though Trump’s effort failed, lawmakers in both parties said his attacks showed the need for stronger safeguards in the law.

The bill would be the strongest legislative response yet to the January 6 attack, in which hundreds of Trump supporters beat police officers, broke into the Capitol and interrupted as lawmakers were counting the votes. Once the rioters were cleared, the House and Senate rejected GOP objections to the vote in two states.

Differences between the House and Senate bills will have to be resolved before final passage, including language on 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 objection in 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. The Senate bill does not.