House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffSchiff claims DHS is blocking whistleblower's access to records before testimony GOP lawmakers distance themselves from Trump comments on transfer of power Rubio on peaceful transfer of power: 'We will have a legitimate & fair election' MORE (D-Calif.) said Tuesday that he hopes House Democrats will resolve the impasse around special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE’s testimony by the end of this week.

Schiff told reporters that Mueller needs to testify “one way or another” before the August recess, whether voluntarily or under subpoena. He also said Mueller could face two subpoenas — one from the Intelligence Committee and another from the Judiciary Committee — for his appearance.

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“We need to resolve this this week, and I hope we will. One way or another, he needs to come in and testify, and time is running out. We want him before the August recess, so we hope to reach a decision this week,” Schiff said when emerging from the Democrats weekly caucus meeting, which was held off-site at the Democratic National Committee headquarters.

Asked if it would be Schiff's Intelligence Committee, or the Judiciary Committee, to issue a subpoena, Schiff said, "Both."

"I don't know that we'd do it jointly. I think we'd probably do two separate subpoenas,” Schiff said.

Schiff floated the possibility that Mueller, who's been clear he doesn't want to appear before Congress, might prefer to be subpoenaed, if only to give him some political cover from accusations that he'd be siding with the Democrats in agreeing to testify voluntarily.

The options, Schiff said, are that Mueller agrees to appear voluntarily or Democrats will issue a subpoena — "unless he would like a subpoena either way."

"But one way or another we expect him to testify," Schiff added.

Rep. Jim Himes James (Jim) Andres HimesMany Democrats want John Bolton's testimony, but Pelosi stays mum SEC's Clayton demurs on firing of Manhattan US attorney he would replace Democrats face tough questions with Bolton MORE (D-Conn.), a member of the Intelligence Committee, said Democrats still insist that Mueller testify publicly.

"It’s important that we get Mueller to speak, and to speak publicly," Himes said. "So whether it's Intel, or Judiciary, or Oversight, I do think we should get Mueller here, and if a subpoena's required we should do it."

Both Schiff and House Judiciary Committee Chairman Jerrold Nadler Jerrold (Jerry) Lewis NadlerDemocrats shoot down talk of expanding Supreme Court Schumer: 'Nothing is off the table' if GOP moves forward with Ginsburg replacement Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence MORE (D-N.Y.) have been negotiating separately for the special counsel to testify before their respective committees for several weeks but have been unable to reach an agreement.

At least part of Mueller’s testimony before the Intelligence Committee would deal with sensitive information and take place in private as a result. Nadler has insisted he wants Mueller's testimony to be public.

Last month, Mueller delivered his first public remarks on his investigation into Russia's election interference, during which he indicated his resistance to testifying publicly before Congress about the two-year probe.

Mueller also said that any public testimony he gave would not go beyond the four corners of his 448-page report, a redacted version of which was released by the Justice Department in April.