White House Press Secretary Stephanie Grisham responded Thursday to former National Security Adviser John Bolton skipping a Trump impeachment inquiry deposition, saying that executive privilege is "very, very important" and that the president "did nothing wrong."

"We have concerns about national security information getting out there. So we'll see what happens. No matter what, no matter who ends up testifying, whether it's behind closed doors or in public, the fact won't change that the president did nothing wrong," Grisham said on "The Story with Martha MacCallum." "So, we're not concerned about that portion of it, but we do want national security matters to stay confidential."

MacCallum asked if the White House would be "supportive" of Bolton if he were subpoenaed and agreed to testify. Grisham responded by saying it "would be up to John Bolton on what he would want to do" before echoing her earlier comments that the president did nothing wrong.

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MacCallum asked Grisham about the president's personal attorney Rudy Giuliani and a report from the New York Times last month saying that Fiona Hill, a former senior director for Russian and Eurasian affairs, allegedly told lawmakers Bolton called the former New York City mayor a "hand grenade" on Ukraine.

Grisham said as far as she knew, Giuliani was still the president's attorney, but declined to address Giuliani or Bolton's alleged comments.

"I don't get into conversations or information about anything that the president does with his personal attorney," Grisham said.

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During the interview, the press secretary dismissed the Washington Post's report that there was "distance" between the president and Attorney General William Barr, calling it more "palace intrigue." She also declined to answer whether Trump would support a potential Senate run by former Trump administration Attorney General Jeff Sessions, saying, "we'll see what happens."

Sessions officially announced his run to represent Alabama in the Senate while appearing on "Tucker Carlson Tonight" shortly after Grisham's interview.

Fox News' Martha MacCallum, John Roberts and Adam Shaw contributed to this report.