"We're not moving on anything," Trump told "Fox & Friends" on Thursday. "We're moving very slowly in one way because we want to make sure it's right."
The Republican blamed the slow progress on former Congressman Beto O'Rourke, who said during last week's Democratic presidential primary debate that he would ensure mandatory buybacks for assault-style rifles if elected, Xinhua reported.
"Part of the problem that we have is because Beto O'Rourke's statement about taking away guns," Trump said.
"All of the moderate Republicans and some Democrats are now afraid to do anything to go down that slippery slope," Trump said.
Trump's remarks came as his administration is reportedly circulating a memo on Capitol Hill describing a possible proposal to expand background checks to all advertised commercial sales, including sales at gun shows.
If someone who attempts to buy a firearm fails a background check, it would be reported to law enforcement officials, according to the memo.
Attorney General William Barr, whose department had drafted the memo, told reporters on Wednesday that the proposal does not have support from the White House.
"I'm up here just kicking around some ideas, getting perspectives so I can be in a better position to advise the president," Barr said. "But the president has made no decision yet."
This past summer, several mass shootings claimed scores of lives in the US, bringing back public attention to the nation's gun violence epidemic while rekindling debates on gun reform.
The House passed a bipartisan background checks bill earlier this year but it still awaits a vote in the Senate.
( With inputs from IANS )