House Democrats have not been counting on Mr. Bolton’s testimony and have signaled that they intend to press ahead with the impeachment inquiry without waiting for court cases about testimony from White House aides to be resolved. Representative Adam B. Schiff, the chairman of the House Intelligence Committee, said Monday that he expected his panel to deliver a report soon after Thanksgiving making the case for impeaching Mr. Trump.

Mr. Bolton was among the most prominent witnesses who did not appear during two weeks of public hearings held by the committee examining Mr. Trump’s efforts to push Ukraine to announce investigations tied to Democrats while withholding $391 million in American security aid.

The former national security adviser, who left his post in September after months of disputes with Mr. Trump on a variety of matters, adamantly opposed the Ukraine pressure campaign, according to testimony before the committee. He referred to it as a “drug deal” cooked up with other advisers to the president and instructed aides to report what they knew about it to White House lawyers.

But Mr. Bolton declined a House invitation to testify after the White House refused to authorize current or former aides to talk with investigators. Instead, he is waiting for the result of a separate lawsuit filed by his longtime friend and former deputy, Charles M. Kupperman, who was subpoenaed in the impeachment inquiry. In October, Mr. Kupperman asked a federal judge to decide whether he should follow the orders of the White House or the House. That case is scheduled to be argued on Dec. 10.

Some Democrats had held out hope that Mr. Bolton might not wait and would instead rely on the decision in the McGahn case to agree to testify. In her ruling, Judge Ketanji Brown Jackson of the Federal District Court for the District of Columbia almost seemed to be addressing Mr. Bolton’s argument that his job was different than that of Mr. McGahn because of its focus on national security matters.

“Nor does it make any difference whether the aides in question are privy to national security matters, or work solely on domestic issues,” she wrote in her 120-page opinion.