"Frankly, we need intelligent background checks," Xinhua quoted Trump as saying to reporters on Friday.
"This isn't a question of NRA, Republican or Democrat," the US President said. The National Rifle Association (NRA) is the most influential gun right lobby group in the country.
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 that he believes there is stronger support for the issue now than following the Parkland high school shooting in 2018.
Two mass shootings killed 31 people 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.
"We're going to have these bipartisan discussions and when we get back (from the Senate summer recess), hopefully, (we'll) be able to come together and actually pass something," McConnell said in an interview with Kentucky radio station WHAS on Thursday.
"Background checks and red flags will probably lead the discussion," said McConnell. "Those are two items that for sure will be front and center as we see what we can come together on and pass."
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 finalised 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 )