Washington (CNN) President Donald Trump told a gathering of state governors on Monday that "we have to have action" in the wake of the latest US mass shooting and urged governors not to be "afraid" of challenging the National Rifle Association.

He also pledged to find a way to eliminate the use of bump fire stocks and called for improving mental health programs.

Trump took turns praising and expressing a willingness to "fight" the powerful gun lobby and said he had pressed the NRA's leaders during lunch over the weekend to back reforms to US gun laws.

"Don't worry about the NRA, they're on our side," Trump said. "Half of you are so afraid of the NRA. There's nothing to be afraid of. ... And you know what, if they're not with you, we have to fight them every once in a while, that's OK. Sometimes we're going to have to be very tough and we're going to have to fight 'em."

Trump said he met over the weekend with NRA CEO Wayne LaPierre and Chris Cox, the head of the NRA's lobbying arm, the two figures who have most prominently pushed the organization's opposition to tightening US gun laws over the years.

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