The White House press secretary said that Mr. Trump had spoken to Senator John Cornyn, Republican of Texas, about legislation he helped introduce to revamp background checks.
WEST PALM BEACH, Fla. — The White House indicated on Monday that President Trump was open to supporting a bipartisan congressional effort to revise federal background checks for prospective gun buyers.
Mr. Trump spoke on Friday to Senator John Cornyn, Republican of Texas, about legislation he helped introduce last fall to revamp background checks, according to the White House press secretary, Sarah Huckabee Sanders. The conversation came after the school shooting last week in Parkland, Fla., that left 17 people dead.
Meeting with victims and with members of that community has appeared to put Mr. Trump in a reflective mood. But the White House stopped short of a full commitment to the bill.
“While discussions are ongoing and revisions are being considered,” Ms. Sanders said in a statement, “the president is supportive of efforts to improve the federal background check system.”
The proposed legislation, introduced by four Republicans and four Democrats in the Senate, would bring significant changes to the national instant criminal background check system. Among other changes, the legislation would hold federal agencies accountable for keeping relevant information out of the database. It would also establish an initiative to better monitor gun buyers with records of domestic abuse.
The lead senators behind the bill — Mr. Cornyn and Chris Murphy, Democrat of Connecticut — have seen some of the worst mass shootings in United States history unfold in their states. A shooting that killed 20 first graders and six adults at Sandy Hook Elementary School in Newtown, Conn., in 2012 came near the beginning of Mr. Murphy’s time in office, and gun restrictions have since been a defining issue for him. And the shooting deaths of more than two dozen people at a church in Sutherland Springs, Tex., in November prompted Mr. Cornyn to co-sponsor the bill with Mr. Murphy.
After the Texas shooting, Attorney General Jeff Sessions asked the F. B. I. to conduct an extensive review of the database because, as he said in a statement at the time, “relevant information may not be getting reported.”
But Congress has been marked by intransigence on gun legislation in recent years, including a failure last year to ban so-called bump stocks, an accessory that the gunman in the Las Vegas shooting in October used to transform his semiautomatic rifles to mimic automatic weapon fire.
Mr. Trump, who has spoken favorably about gun rights over the years, has held wavering views on gun restrictions in the past. He had a concealed weapon permit in New York when Rudolph W. Giuliani was mayor, but it is not clear whether he maintained it.
In 2000, as he considered running for president, Mr. Trump wrote in his book, “The America We Deserve,” that “I generally oppose gun control, but I support the ban on assault weapons and I also support a slightly longer waiting period to purchase a gun.”
He added, “With today’s internet technology we should be able to tell within 72 hours if a potential gun owner has a record.”
In a 2016 appearance on CNN, Mr. Trump said that he thought guns should not be allowed in classrooms, and then followed up moments later by saying that some teachers should have access to firearms.
“You look at some of our schools, unbelievable what’s going on, but I’m not advocating guns in the classroom,” Mr. Trump said at the time. “Remember in some cases, a lot of people admit this, trained teachers should be able to have guns in classrooms.”
