At one point, he even suggested a conversation on an assault weapons ban.
The tug of war over the appropriate response on the school shooting remains far from settled.
Prior to the meeting, four Democratic senators led by Minority Leader Chuck Schumer of NY, urged Trump to support background checks on all gun sales that "closes those loopholes for good".
Both the National Rifle Association and the White House made statements that suggest President Donald Trump isn't as firm on gun restrictions as he himself made it sound.
The exhortation to Trump, who this week stunned fellow Republicans by backing several gun control measures his party has long opposed, reflected a fierce tug-of-war for the president's support on gun measures in the wake of a deadly February 14 high school shooting in Florida.
Cornyn's bill, which has bipartisan support, would offer incentives to federal and state agencies to file already required reports with the FBI's National Instant Criminal Background Check System, known as NICS, to block ineligible gun purchasers with felonies or unsafe mental illness.
Another one of Trump's modest proposals is that the age limit should be raised on certain types of guns.
He called for Trump's assistance in passing a gun-control measure, as Trump had publicly voiced support for each of the Democrats' proposals. The bottom line appears to be that Trump now supports Sen. John Cornyn and Chris Murphy though he could possibly go beyond that. The president wants to improve the current system but is "not necessarily" in favor of background checks for all gun purchases, she said.
"I'm hoping there's a way forward", he told reporters as lawmakers left Washington. Lawmakers had been making incremental progress on a bill to boost participation in the existing federal background check bill.
Just what Trump would like to see in the "beautiful" and "comprehensive" bill he called for earlier in the week remained unclear.
But Mr Trump kept mostly quiet on the subject Thursday.
The Senate more likely will turn to a bipartisan bill from Sens.
"As of right now, he supports the Cornyn legislation". The measure, from Sens. Pat Toomey (R-Pa.) of being "afraid" of the NRA.
He's calling for substantial changes in the nation's gun laws - a position he pushed during a White House meeting with a bipartisan group of lawmakers.
"Not having background checks at gun shows is like checking IDs at the liquor store but not the bar - it makes no sense", he said. And he backs more contentious ideas, like increasing the minimum age for the purchase of assault-style weapons from 18 to 21, an idea opposed by the NRA.
"We can't wait and play games and nothing gets done", Trump told the session with 17 House and Senate lawmakers.
President Donald Trump speaks in the Cabinet Room of the White House, in Washington, Wednesday, Feb. 28, 2018, during a meeting with members of congress to discuss school and community safety.
Trump has previously said that violent games may act as the main cause of school shootings.
Senate Minority Leader Chuck Schumer and other top Democrats are now urging the President to help pass the measure in the wake of the Florida high school shooting. "But we can't do it alone".
Trump has mentioned arming teachers, and says his administration, not Congress, would ban bump-stock devices that enable guns to fire like automatic weapons.
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