The executive director of the National Rifle Association, Chris Cox, also tweeted about the meeting, saying Trump, Vice President Mike Pence and the NRA "want safe schools, mental health reform and to keep guns away from risky people".
At the end of a wide-ranging White House meeting Wednesday with congressional lawmakers on how to toughen gun laws, Trump urged Pennsylvania Sen.
Several Republican lawmakers spoke up on social media and in other forums to push back on that notion, as well as Trump's advocacy for stronger background checks and a higher minimum age for rifle purchases - taking it from 18 to 21, the current minimum age for handgun purchases.
The bill President Trump is referring to involves the expansion of background checks. His comments suggested that, after a school shooting in Parkland, Florida, left 17 people dead and sparked a youth movement for gun control, he was interested in breaking with the gun-rights group on key issues.
"It would be so handsome to have one bill", Trump told lawmakers at the outset. They're still working out some of the final pieces of that legislation, and until it gets to the final stage, we're not going to weigh in.
In the made-for-TV event on Wednesday, Trump struck a moderate tone and encouraged a group of Republicans and Democrats to act quickly on a comprehensive gun reform package.
Trump and Cornyn had talked multiple times this week about guns, multiple sources told CNN. "The White House can now launch a lobbying campaign to get universal background checks passed as the president promised in this meeting, or they can do nothing", he added. John Cornyn, R-Texas, and Chris Murphy, D-Conn., that would require federal and state agencies to report relevant criminal history records to the National Instant Criminal Background Check System. "But we haven't made a final determination", Sanders said.
"The president said a lot of things right yesterday..."
And Trump received the most shocked reactions when he said it might be better in some cases to allow law enforcement to confiscate weapons from potentially disturbed individuals before allowing those individuals due process through the courts.
Separately Thursday, House Minority Leader Nancy Pelosi, D-Calif., told reporters that she was "encouraged" by the White House meeting and "optimistic" that Trump would take action.
Mr. Trump ran as a staunch defender of gun rights and an ally of the NRA.
The president has previously supported ideas popular with Democrats, only to back away when faced with opposition from his conservative supporters and his GOP allies in Congress.
For example, one of the sources said the plan was to roll out a policy that would make it easier for a judge to weigh in on whether someone with a mental illness should have a firearm.
Friday capped a week of conflicting signals from Trump and the White House on what the president wants to do in response to the shootings in Florida, which has led to confusion over what policies he wants Congress to advance.
The President also said that he will unilaterally ban so-called "bump stocks", which is an attachment that enables a semiautomatic rifle to fire faster.
A statement provided to Business Insider by the Entertainment Software Association, the trade association that represents the video game industry, said that no video game company had recieved an invitation to any such White House meeting.