(CNN) — Senate Minority Leader Mitch McConnell announced Tuesday he would support legislation that would make it harder to overturn a certified presidential election, an endorsement that will bolster its chances for passage in his chamber and puts him at sharp odds with former President Donald Trump, who has called on GOP senators to sink the plan.

McConnell said the “chaos” of the pro-Trump attack on the Capitol last year “certainly underscored the need for an update.”

“I strongly support the modest changes that our colleagues in the working group have fleshed out after literally months of detailed discussions,” McConnell said. “I’ll proudly support the legislation, provided that nothing more than technical changes are made to its current form.”

“Congress’ process for counting the presidential electors’ votes was written 135 years ago. The chaos that came to a head on January 6th of last year certainly underscored the need for an update,” added McConnell. “So did Januaries 2001, 2005 and 2017. In each of which, Democrats tried to challenge the lawful election of a Republican president.”

Last week, House GOP Leader Kevin McCarthy and the vast majority of House Republicans opposed their chamber’s version of the bill that would amend the Electoral Count Act of 1887. While the House bill has a number of similarities with the Senate’s version, including ensuring the vice president only has a ministerial role in overseeing a joint session of Congress approving state-certified electoral results, it differs in some of its details. Among the differences: The number of lawmakers who would be required to force the House and Senate to vote to overturn a state’s certified electoral results and the procedures for resolving election disputes in federal courts.

Maine Republican Sen. Susan Collins and West Virginia Democratic Sen. Joe Manchin have already lined up 10 Republican co-sponsors for their so-called Electoral Count Reform and Presidential Transition Improvement Act, enough support to surpass a filibuster with 50 Democratic votes.

The Senate bill would make a number of changes to the Electoral Count Act, and the Presidential Transition Act of 1963, in an attempt to address ambiguity in electoral law that Trump tried to exploit.

It would increase the number of House and Senate members required to raise an objection to election results when a joint session of Congress meets to certify them. One House member and one senator can currently object to electoral votes, sending them to a vote in Congress; If either chamber rejects the objection, the votes are counted. The Senate bill would require the support of one-fifth of each chamber to raise an objection. The House bill would raise the threshold even higher — to one-third of each chamber — to force both chambers to vote on whether to throw out a state’s electoral results.

In an effort to respond to Trump allies who tried to send fake electors to Congress, both bills try to make it harder for there to be any confusion over the electors themselves. In the Senate bill, it states that each state’s governor would be responsible for submission of a certificate that identifies electors, eliminating the potential for multiple state officials sending multiple slates of electors. But the bills differ in how lawsuits challenging election results can be taken up in federal court, with the House bill offering new avenues to sue, something some key Senate Republicans oppose.

In a clear response to Trump’s efforts to get then-Vice President Mike Pence to reject the electoral results of states that President Joe Biden won, both bills establish the vice president’s role as purely ceremonial. The Senate bill would deny the vice president the power to “solely determine, accept, reject, or otherwise adjudicate or resolve disputes over the proper list of electors, the validity of electors, or the votes of electors.”

While constitutional experts say the vice president currently can’t disregard a state-certified electoral result, Trump pushed Pence to obstruct the Electoral College certification in Congress. But Pence refused to do so and, as a result, became a target of the former President and his mob of supporters who stormed the Capitol on January 6, 2021.

The Senate’s bill has been split into two separate proposals, one of which will be voted on by the Senate Rules Committee on Tuesday. The other package will go before the Senate Homeland Security and Governmental Affairs, which has yet to consider the measure. The full Senate is unlikely to act before the November midterms, punting the issue until a lame-duck session of Congress at year’s end.

It remains uncertain if both chambers can reconcile their differences or if the House will be forced to simply accept the Senate’s version. Some House Republicans who opposed their chamber’s bill — drafted by California Democratic Rep. Zoe Lofgren and Wyoming Republican Rep. Liz Cheney — objected to how it did not go through the committee process and signaled they could support the Senate’s plan instead.

“The resulting product — this bill, as introduced — is the only chance to get an outcome and to actually make law,” said McConnell on Tuesday. “It keeps what’s worked well and modestly updates what has not.”