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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.”

According to the Washington Post, which first reported on the details of a Tuesday call, LaPierre told Trump that support for a background check bill from Sens. Pat Toomey and Joe Manchin would not be favored among Trump’s base and argued against the bill’s merits.

Toomey and Manchin’s expanded background check bill from 2013 was opposed by the NRA, which claimed that the legislation would “not prevent the next shooting.”

However, the day after his initial call with LaPierre, Trump told reporters that he’ll be working with Congress on legislation to address mass shootings, starting with background checks and mental illness.

“Well I’m looking to do background checks. I think background checks are important. I don’t want to put guns into the hands of mentally unstable people or people with rage or hate,” Trump said on Wednesday, before leaving for his visits to El Paso and Dayton.

Democrats have called for the President and Republican leaders to act on legislation in the wake of the two shootings, which left more than 30 dead. A source familiar with internal discussions told CNN that Trump is looking at ways to tighten up background checks through some sort of executive action, but the source cautioned it’s too early in the process to get into any more detail.

Last year, Trump signed the Fix NICS Act, which, among other things, awards funds to states that voluntarily provide information on individuals for the National Instant Criminal Background Check System database. But the law did not prevent the mass shootings this weekend because there is currently no evidence that the two alleged shooters were legally prohibited from owning firearms.

Trump has previously expressed support for tighter gun restrictions – particularly in the wake of last year’s Parkland, Florida, high school shooting – only to back off under pressure from the NRA.

Counselor to the President Kellyanne Conway said earlier this week in an interview with Fox News that “the President stands ready to act” and is “willing to do things that keep the guns out of the hands of the wrong people, without abrogating the rights of citizens” to have weapons.

She added that Trump had spoken with Toomey, a Pennsylvania Republican, and Manchin, a West Virginia Democrat, about their background check legislation.

A mid-July NPR/PBS NewsHour/Marist poll found that 89% considered it a “good idea” to implement background checks for gun purchases at gun shows or other private sales, with a nearly nonexistent partisan divide: 96% of Democrats, 89% of independents and 84% of Republicans called it a good idea.

This story has been updated.

CNN’s Jim Acosta, Kevin Liptak and Nikki Carvajal contributed to this report.