They also wanted Hicks to talk about five examples of potential obstruction of justice by Trump that are laid out in Mueller's report, as well as the president's efforts to impede the Mueller investigation.
Hicks, who was subpoenaed to testify, was part of Trump's inner circle as one of his longest-serving and most trusted advisers. The committee announced Hicks' agreement to appear last week and has said it plans to release transcripts from the hearing shortly after its conclusion.
Representative Doug Collins of Georgia, the panel's top Republican, said Democrats seem to be gearing up "a summer of reruns", rehashing and "relitigating" matters already explored in greater depth by Mueller.
It was unclear how much new information Hicks will provide.
Democrats say her appearance could help undermine Trump's strategy of stonewalling congressional investigators by encouraging others to co-operate with them and by giving investigators the chance to challenge any executive privilege assertions, possibly in federal court.
Cipollone said Hicks, as one of Trump's former senior advisers, is "absolutely immune" from compelled testimony with respect to her service to the president because of the separation of powers between the executive and legislative branches.
Former White House Counsel Don McGahn, a star witness in the Mueller report, last month defied a subpoena for his testimony and documents after the White House directed him not to co-operate with the Judiciary panel.
Hicks worked for Trump before he declared his bid for office, served as press secretary on the Trump campaign and then served as White House communications director. "But Hope Hicks is listening to what they're saying in terms of objections, so she doesn't answer", U.S. Representative Ted Lieu said.
More than 60 lawmakers in her caucus - including nearly a dozen on the committee - have called for opening an impeachment inquiry, but she has said she wants committees to investigate first and come to a decision on impeachment later.
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She did not answer when asked how she would respond to committee questions.
Despite the closed setting, Democrats, who control the House of Representatives, view Hicks' appearance as a breakthrough for their congressional investigation, which could trigger impeachment proceedings against the president if it unearths evidence of serious misconduct. She agreed to provide some information from her work on Trump's campaign, according to the committee, but none from her time at the White House. That includes the president's role in the drafting of a misleading and incomplete statement about a 2016 Trump Tower meeting at which Trump's son, Donald Trump Jr., expected to receive dirt on Democrat Hillary Clinton. It also described numerous attempts by Trump to impede Mueller's investigation but stopped short of declaring that he committed a crime. On Wednesday she said if the investigations find criminal wrongdoing, the path would be clear.
Mueller wrote in his 448-page report released in April that there was not enough evidence to establish a criminal conspiracy between Trump's 2016 campaign and Russian Federation, but he said he could not exonerate Trump on obstruction of justice.
Lawmakers also wanted to ask Hicks about former national security adviser Michael Flynn's ouster, the president's decision to fire FBI Director James Comey, his efforts to thwart special counsel Robert Mueller's almost two-year investigation and a meeting at Trump Tower in the summer of 2016 that included Mr. Trump's son, Donald Trump, Jr., top campaign officials and a Russian lawyer Trump Jr. thought had damaging information about Hillary Clinton.
Hicks is the first senior administration official cited frequently in special counsel Robert Mueller's report to testify before the committee. The aides spoke on condition of anonymity to discuss their plans for the closed-door meeting.
Democrats on the committee wanted to hear from Hicks about alleged hush money payments made during the campaign to two women, including porn star Stormy Daniels, who say they had affairs with Trump. Trump has denied the allegations.
Republicans have strongly criticized the investigations and say they are unnecessary after Mueller spent two years reviewing the same material and talking to the same witnesses. Cohen - who pleaded guilty to a campaign finance violation in connection with the episode a year ago - said the deal was arranged at Trump's direction.
They also plan to use the information from Hicks' interview as part of their second hearing into the contents of the Mueller report, which is slated for June 20.