Pelosi and Schumer, in Push for Gun Safety Legislation, Urge Trump to Defy N.R.A.

Yet some Republicans, especially in states where there have been mass shootings, are also calling for gun safety legislation. In Texas, where there were multiple deadly shootings in August, Lt. Gov. Dan Patrick, a staunch proponent of gun rights, called on Friday for background checks on private gun sales.

In Washington, the August shootings prompted Republicans to quickly rally around another type of gun control legislation: so-called red flag laws, which make it easier for law enforcement to take guns away from people deemed dangerous by a judge. In the Senate, Lindsey Graham, Republican of South Carolina, and Richard Blumenthal, Democrat of Connecticut, are sponsoring a red flag bill.

The massacres also revived talk of the bipartisan background checks bill known as the Manchin-Toomey bill, after its Senate sponsors, Joe Manchin III, Democrat of West Virginia, and Patrick J. Toomey, Republican of Pennsylvania. But the legislation, which includes exemptions for gun transfers for family members and friends, is not as expansive as the House bill, and many Republicans remain uncomfortable with it. It fell to a Senate filibuster in 2013.

At the direction of Mr. Trump, top White House officials have been engaged in bipartisan talks with lawmakers, including Mr. Manchin and Mr. Toomey, about what kind of gun legislation the president might be willing to support — and what Democrats would agree to.

An administration official participating in the talks, who spoke on the condition of anonymity because he was not authorized to disclose internal deliberations, said after a recent deadly shooting spree in West Texas that they were making “a lot of progress in good faith,” but had reached no agreement. On Sunday, the official said the status of the talks was unchanged.

Mr. McConnell, meanwhile, has directed three top committee chairmen in the Senate — Mr. Graham of the Judiciary Committee, Lamar Alexander of the health committee and Roger Wicker of the commerce committee — to engage in “bipartisan discussions of potential solutions to help protect our communities without infringing on Americans’ constitutional rights.”

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