Washington (CNN) President Donald Trump is facing pressure from the National Rifle Association over his openness to expanding background checks in the wake of last week's deadly mass shootings in Texas and Ohio.

Trump has spoken to NRA chief executive Wayne LaPierre multiple times over the last two days, a person familiar with the conversations tells CNN. In those conversations, LaPierre made clear the NRA's stance on renewed calls for expanded background checks -- something the President has privately and publicly supported in recent days.

The NRA chief stressed to Trump that they don't think the calls for more restrictive gun measures in Washington match how his supporters in deep red areas feel about the issue, the person said.

Reflecting that conversation, the gun lobby group tweeted on Thursday that "the NRA's long-standing position that those who have been adjudicated as a danger to themselves or others should not have access to firearms and should be admitted for treatment."

"But, there needs to be real evidence of danger -- and we cannot sacrifice anyone's constitutional rights without due process," the organization said in a series of tweets. "It is not enough anymore to simply say that 'we need more background checks.' Considering both suspects in El Paso and Dayton passed them, that is rhetoric for billionaire activists and campaign rallies -- not a call for constructive progress."