(CNN) The House of Representatives says it no longer needs to subpoena former deputy national security adviser Charles Kupperman for his testimony, another sign that Democrats don't want or feel they need a prolonged battle to gather more details in their impeachment probe.

"The subpoena at issue in this matter has been withdrawn and there is no current intention to reissue it," the House wrote in a court case filed on Wednesday afternoon about Kupperman's testimony.

The House instead suggested Kupperman should abide by what is decided in a separate case that is further along: its lawsuit against Don McGahn to force the former White House counsel to testify.

The House told Kupperman's attorney on Tuesday it still would be interested in speaking with him in the impeachment inquiry, and that he should sit for a deposition if another federal judge knocks down the White House's blocking tactic in McGahn's case. McGahn was subpoenaed in April to discuss the President's attempts to obstruct the Russia investigation.

McGahn's case is "much closer to resolution by the court than Dr. Kupperman's flawed suit," the House wrote to Kupperman's attorneys on Tuesday. "Unless your lawsuit was admittedly only for purposes of delay, and without a subpoena in force, the Committees expect that your client will voluntarily dismiss the complaint ... and be guided by the decision in McGahn."

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