US President Donald Trump said Wednesday that all "mentally stable" Americans should be able to own firearms amid reports he retreated on plans to toughen gun purchase background checks in the wake of a string of mass shootings.

"I want guns in the hands of people that are mentally stable," Trump told reporters.

"Those people, I want them to be easily able to get a gun. But people who are insane, people who are sick... I don't want them to be able to get a gun."

Trump denied media reports that on Tuesday he had promised National Rifle Association head Wayne LaPierre that he would not press Congress for a law tightening background checks on people seeking to purchase guns.

Several leading media outlets including the Washington Post and The Atlantic quoted White House sources as saying Trump promised LaPierre he would not pressure Congress for a stringent, universal, pre-sale review of all gun buyers.