WASHINGTON — A leading Senate ally of President Donald Trump introduced a resolution Thursday condemning the Democratic-run House for pursuing an “illegitimate impeachment inquiry” and demanding that Republicans be given more chances to question witnesses.

After two dramatic days of closed-door depositions, House investigators paused for a service in the Capitol in honor of the late congressman Elijah Cummings, D-Md., the former House Oversight and Reform Committee chairman.

But debate over the fairness of the inquiry continued unabated, with Trump praising House Republicans for storming a secure room where dispositions are being held and House Speaker Nancy Pelosi, D-Calif., accusing GOP lawmakers of “covering up” for a president abusing his power.

The nonbinding resolution announced by GOP Sen. Lindsey Graham of South Carolina gives Senate Republicans a chance to show support for Trump at a moment when the president is urging his GOP allies to fight harder for him as the House impeachment probe gathers momentum.

Graham said the House process has been “a star-chamber-type inquiry” and accused Democrats of using it to damage Trump.

“If you can drive down a president’s poll numbers by having proceedings where you selectively leak information, where the president who’s the subject of all this is pretty much shut out, God help future presidents,” Graham told reporters.

Democrats, meanwhile, are looking to make the proceedings public by mid-November as they build a case about Trump pressing Ukraine to investigate former Vice President Joe Biden and his son Hunter while U.S. military aid to the country was being withheld.

After urging House Republicans earlier this week to “get tough and fight,” Trump took to Twitter on Thursday to praise them after about 30 GOP lawmakers stormed the secure room Wednesday.

“Thank you to House Republicans for being tough, smart, and understanding in detail the greatest Witch Hunt in American History,” Trump tweeted. “It has been going on since long before I even got Elected (the Insurance Policy!). A total Scam!”

Rather than attacking the substance of the evidence investigators are accumulating, Republicans have focused on asserting that House impeachment proceedings have been secretive and unfair.

With lawmakers from both parties present, House investigators have been questioning diplomats and administration officials behind closed doors for several weeks.

Should the House vote to impeach Trump, both sides would be able to question witnesses in the GOP-run Senate.

Senate Minority Leader Chuck Schumer, D-N.Y., accused Republicans of hypocrisy by claiming they want an open process while the White House defies subpoenas, refuses to surrender documents and tries blocking officials from testifying.

“Rather than stomp their feet in a fit of staged political theater, House Republicans — all Republicans — should join in getting all the facts,” he said.

Senate Majority Leader Mitch McConnell, R-Ky., is a leading co-sponsor of the measure. Asked about a vote, McConnell said earlier Thursday that Republicans are “discussing the way forward on that.”

Later Thursday, Graham said 44 of the Senate’s 53 Republicans had co-sponsored the resolution. That included two of the four GOP senators expected to face the most competitive elections next year: Thom Tillis of North Carolina and Martha McSally of Arizona.

Meanwhile, a Defense Department official who testified in the impeachment inquiry did so in defiance of the Pentagon, which told her not to cooperate. A letter to Laura Cooper’s attorney obtained by the AP cites an administration-wide policy against participating in the impeachment probe.

The directive underscores Trump administration efforts to discourage executive branch employees from cooperating with House Democrats. The administration this month blocked Gordon Sondland, the ambassador to the European Union, from testifying, though he ultimately did so under subpoena.

The letter cites concerns about whether the House is authorized to conduct an impeachment inquiry without a formal vote and about what it says is a “blanket refusal” to permit Defense Department lawyers from being present for the interviews. Excluding department lawyers, the letter said, “violates settled practice and may jeopardize future accommodation.”

“To reiterate, the Department respects the oversight role of Congress and stands ready to work with the Committees should there be an appropriate resolution of outstanding legal issues,” reads the Defense Department letter to Cooper’s lawyer, Daniel Levin.

But, it adds, “Any such resolution would have to consider the constitutional prerogatives and confidentiality interests of the coequal Executive Branch and ensure fundamental fairness to any Executive Branch employees involved in this process, including Ms. Cooper.”

The Washington Post contributed.