(CNN) - President Donald Trump capped a week of see-sawing statements on gun control proposals by claiming Thursday evening that bipartisan talks are ongoing.
Following back-to-back mass shootings in El Paso, Texas, and Dayton, Ohio, earlier this month, Trump issued a call for stricter background checks. But in the last week, Trump has fallen into a similar pattern he's followed in the wake of mass shootings under his watch, cooling to the idea of background checks.
"Talks are ongoing (with) both Republicans & Democrats. We are likewise engaging with lawful gun owners, survivors, grieving family members, law enforcement, the NRA, mental health professionals, and school officials," Trump tweeted on Thursday night. "I am hopeful Congress will engage with my Team to pass meaningful legislation that will make a real difference and, most importantly, Save Lives!"
Connecticut Democratic Sen. Chris Murphy, confirmed Thursday that he spoke with the White House about the issue, saying that "they have not walked away from improving background checks."
"I am skeptical we can reach consensus but I'm willing to stay at the table over next few weeks. Maybe I'm a fool for trying but stakes are too high," Murphy said.
The Thursday meeting and call with Murphy follow a week of Trump's retreats on the issue.
This week Trump has pivoted to focusing on mental health and, according to a source familiar with the conversation, the President told National Rifle Association chief Wayne LaPierre Tuesday that universal background checks are "off the table."
Trump has also indicated in conversations with lawmakers that he's cooled to the idea of expanded background checks, congressional and Republican sources told CNN.
Trump said Wednesday that there is an "appetite for background checks" and wants to fix loopholes, but reiterated several times to reporters on the south lawn his belief that the US "already" has "strong" background checks.
Trump added that he is "concerned" that whatever Democrats and Republicans agree to in respect to gun control, Democrats will always want more, saying, "that's a slippery slope."
When asked why anyone who wants to buy a gun shouldn't have to go through a background check, Trump responded: "What we're doing is I want guns to be in the hands of people that are mentally stable and those people I want them to be easily be able to get a gun. But people that are insane, sick up here, I don't want them to be able to get a gun."
Any company or shop that sells guns must put buyers through a background check. However, in the majority of states, private sellers -- those who occasionally sell guns they own and are not trying to turn a profit -- do not have to submit a buyer to the federal background check system.
CNN's Allie Malloy, Kaitlan Collins, Jim Acosta and Holmes Lyband contributed to this report.
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