"Frankly, we need intelligent background checks," Trump told reporters on Friday as he left the White House for a fundraiser in the Hamptons, New York.
"This isn't a question of the NRA (National Rifle Association), Republicans or Democrats," the President said.
The NRA is the most influential gun right lobby group in the country, Xinhua news agency reported.
Trump said he had spoken with Senate Majority Leader Mitch McConnell, Senate Minority Leader Charles Schumer and Speaker Nancy Pelosi about gun legislations.
"I think we can get something really good done. I think we can have some meaningful background checks," Trump said, adding he believed that there was stronger support for the issue now than the Parkland high school shooting in 2018.
The two mass shootings took place within 13 hours over the weekend in El Paso, Texas and Dayton, Ohio, invoking pain and anger at the country's leadership for its inaction after the repeated attacks.
The Democratic-led House passed two gun bills in February.
One is aimed at closing loopholes that have allowed some sales over the Internet and at gun shows to be finalized without background checks, and the other would extend to 10 business days, from the current three, the amount of time for background checks if information on a gun sale application is incomplete.
In a joint statement on Thursday, Pelosi and Schumer said Trump called them individually earlier on the day, assuring them that he will review the House-passed gun bills.
( With inputs from IANS )