WASHINGTON — A moderate Republican senator sought broad bipartisan support Tuesday for a compromise to block gun purchases by some suspected terrorists, a day after the chamber split along party lines to derail far more sweeping proposals.

Senate Majority Leader Mitch McConnell, R-Ky., said he would allow a vote on the proposal by Sen. Susan Collins, R-Maine, but stopped short of endorsing the measure itself. The package seemed to face an uphill climb for the 60 votes it would need, due to the hurdles of election-year politics and opposition from the National Rifle Association and Gun Owners of America.

Collins told reporters that mass shootings in Orlando, Fla., and San Bernardino, Calif., were “a call for compromise, a plea for bipartisan action.”

“If we can’t pass this, it truly is a broken system up here,” said Sen. Lindsey Graham, R-S.C.

On Monday, the Senate rejected rival Democratic and Republican proposals for keeping guns from known and suspected terrorists. President Barack Obama criticized the stalemate Tuesday, tweeting: “Gun violence requires more than moments of silence. It requires action. In failing that test, the Senate failed the American people.”

The government’s overall terrorist watch list has 1 million people on it. Collins’ measure would let federal authorities bar gun sales to two narrower groups: the no-fly list with 81,000 people and the selectee list with 28,000 people. Selectees can fly after unusually intensive screening. All but a combined total of around 2,800 people on those lists are foreigners, who are mostly unable to purchase firearms in the U.S.

The FBI would be notified if someone who’s been on the broader terrorist watch list in the past five years buys a gun, but could not stop the purchase.