President Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE told Sen. Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Utah) on Thursday that he does not support a House-passed surveillance bill— raising fresh questions about the fate of the legislation.

A spokesman for Lee confirmed the conversation and that the president told the Utah Republican that he does not support the House legislation. Officials speaking for the White House did not immediately respond to a request for comment.

Lee and Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) have been working to kill the House bill, including urging Trump to veto it if it reaches his desk, over concerns that it does not go far enough to reform the court associated with the Freedom Intelligence Surveillance Act (FISA).

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Lee tried, but failed, to get the Senate to pass a 45-day extension of three soon-to-expire provisions of the USA Freedom Act, as well as guarantee votes on amendments to the House legislation, which pairs a reauthorization of the provisions with some changes to the FISA process.

Progressives and libertarian-minded GOP senators have warned for years that they do not believe the surveillance court provides enough transparency or privacy protections for the targeted.

They've been joined by several Republican lawmakers after the Justice Department inspector general Michael Horowitz found 17 significant inaccuracies and omissions as part of the warrant applications into Trump campaign associate Carter Page.

Trump has repeatedly railed against FISA, arguing that his campaign was "spied" upon.

He appeared to signal on Thursday that he was open to their argument when he tweeted on Thursday that some Republicans were urging him to veto the legislation.

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“Many Republican Senators want me to Veto the FISA Bill until we find out what led to, and happened with, the illegal attempted ’coup’ of the duly elected President of the United States, and others!” he tweeted.

Lee — whose conversation with Trump was first reported by The Wall Street Journal — seized on the president's tweet during a lengthy floor speech where railed against the House bill.

"He still has concerns with FISA and that many senators are pointing out the flaws in the reforms package passed by the Democratic-controlled House of Representatives this week, that many have encouraged him to veto that legislation," Lee said. "If the president of the United States himself has reason to be concerned about FISA, what about the rest of Americans?"

A White House official told The Hill that the president is interested in significant FISA reforms but is “carefully listening” to views of all Republicans.

“There is a lot of interest in the significant reform that conservatives drove to completion to address the abuses of FISA against him and other innocent members of the 2016 campaign,” the official said.

Morgan Chalfant contributed.