“The public must weigh in and demand passage of this legislation for the safety of our children," they continued.

“It took less than three hours for the president to back off his call for stronger background check legislation. When he can’t talk about guns when he talks about gun violence, it shows the president remains prisoner to the gun lobby and the NRA," the two Democratic leaders said in a joint statement, referring to the National Rifle Association.

Speaker(D-Calif.) and Senate Minority Leader(D-N.Y.) on Monday knocked's remarks on two recent mass shootings, saying he is a "prisoner to the gun lobby and the NRA."

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Trump, during an address from the White House earlier Monday, urged the country to condemn white supremacy and endorsed new measures focusing on mental illness, rather than stricter gun laws.

Trump said in a tweet earlier Monday that he supported "strong background checks," but he didn't mention the proposal in his remarks.

The House passed gun control legislation in February to require universal background checks, but the bill has stalled in the GOP-controlled Senate, where any gun-related legislation faces an uphill climb to get a vote, much less passage.

“However, Senate Republican Leader Mitch McConnell has called himself the ‘grim reaper’ and refuses to act on this bipartisan legislation. It is incumbent upon the Senate to come back into session to pass this legislation immediately," Pelosi and Schumer added in their joint statement on Monday.

The Senate is currently set to return to Washington on September 9.

A spokesman for McConnell, who fractured his shoulder over the weekend, didn't immediately respond to a request for comment about calls for the chamber to reconvene.

Trump did outline other possible steps, including a "red-flag" law that would make it easier for law enforcement to identify mentally ill people who should be banned from purchasing guns. Trump also said people who commit deadly hate crimes should be punished with the death penalty in a “quick and decisive” way.