On Twitter Tuesday, Trump reiterated his protection of Haspel as robust on terror.
In the ad, CIA director nominee Gina Haspel is described as "a decorated intelligence officer admired by allies around the globe with bipartisan support".
During the phone call, Trump dismissed concerns about Haspel's role in past interrogations of suspected terrorists and voiced support for her nomination, a separate source said. "It's fantastic to watch the media disparage and attack women of real substance while they laud a woman who spends most of her time hanging off a pole half or completely naked".
Charging a "lack of transparency", Senator Mark Warner made the request two days before the panel holds a confirmation hearing where Gina Haspel will face questioning about her history with the Central Intelligence Agency program that used interrogation methods denounced as torture. This is when she offered to withdraw, the officials said.
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Trump said he thought Tester would have a "big price to pay in Montana" over the accusations against Jackson. In a tweet Monday, Trump said Haspel "has come under fire because she was too tough on Terrorists".
The CIA responded by saying it had sent more classified documents to the Senate covering her "actual and outstanding record", beginning with her work for the agency's Counter-Terrorism Center after the September 11, 2001, attacks. He said a memo drafted by Haspel calling for the destruction of interrogation tapes - which were shredded in 2005 - was ordered by Rodriguez and that she believed Rodriguez would seek permission from then-CIA Director Porter Goss before carrying it out. Senators had demanded greater transparency from the CIA over her history and on Monday the agency delivered a cardboard box full of classified documents. As of this writing, Republicans own a 51-49 majority in the Senate, which means she has enough votes to be confirmed if every Republican votes for her and if no Democrats vote for her.
"Acting Director Haspel is a highly qualified nominee who has dedicated over three decades of service to her country", he said in a statement provided to CBS News. The news was first reported Sunday by The Washington Post. She told reporters the sessions had been "great".
The White House is pressuring lawmakers to confirm Ms Haspel.
In the less than two months since Haspel's nomination to replace Mike Pompeo, now secretary of State, was announced, the deputy has faced increased scrutiny over her past. By Saturday she had reportedly agreed to continue with the nomination.