House Republicans on Wednesday stormed the secure room where lawmakers have been conducting the impeachment probe against President Trump, upending a scheduled deposition as they demanded fairness from the Democrats running the show.

The move enraged Democrats, who said as part of their protest the Republican lawmakers carried electronics into the secure area, creating a potential security lapse. They demanded the 30 or so Republican protesters face ethics charges.

GOP lawmakers brushed those complaints aside, saying the hearing they disrupted, involving Defense Department official Laura Cooper, was not classified, and saying Democrats have broken the rules of fairness by shutting them out of the impeachment process.

“House Democrats are bypassing constitutional norms and basic standards of due process with their impeachment obsession,” said Rep. Mark Walker, North Carolina Republican. “The president is not above justice. But, as you know, neither is he below it.”

Another Republican, Rep. Debbie Lesko of Arizona, was more direct.

“This is an outrage,” she said.

The Democrats’ impeachment inquiry into Mr. Trump’s communications with Ukraine over former Vice President Joseph R. Biden, a political opponent, is not following any of the precedents for impeachment proceedings.

Mr. Trump’s lawyers have been denied the chance to see evidence or call their own witnesses, and Republicans have been denied subpoena power. The work of the impeachment committees has been restricted, even from some Republican members of those committees.

Wednesday’s protest involved lawmakers who aren’t on the impeachment committees but who say under House rules they have a right to see what’s going on.

Democrats counter that Republicans on the committees can participate and ask questions, and that is good enough.

“This investigation is being conducted by the Intelligence Committee, and members of the Republican side were there if they chose to be during the depositions and they certainly were permitted to ask whatever questions they wanted to,” said Rep. Val Demmings Florida Democrat. “They have access to transcripts and information that were available.”

House Intelligence Committee Chairman Adam B. Schiff, California Democrat, threatened to bring ethics charges against the Republican protesters, and Homeland Security Committee Chairman Bennie G. Thompson asked the sergeant at arms to probe the breach of the room, known as a Sensitive Compartmented Information Facility or SCIF.

Rep. Eric Swalwell, California Democrat, said the problem was that lawmakers brought in electronic devices, which are usually banned.

“And they not only brought in their unauthorized device, they may have brought in the Russian and Chinese with electronics in a secure space,” Mr. Swalwell said.

Ms. Schiff shut down the questioning of Ms. Cooper during the GOP protest, which turned into an hours-long sit-in.

Ms. Cooper ultimately did testify, five hours after she was scheduled to begin.

Members on both sides were mum on the details of what she said.

Her testimony comes a day after a former U.S. diplomat to Ukraine told lawmakers that Mr. Trump made the release of military aid to Ukraine contingent on that country probing Mr. Biden and his son Hunter, who was on the board of directors of Ukrainian energy company Burisma.

That diplomat, William Taylor, said he uncovered an “irregular” backchannel managed by Mr. Trump’s personal attorney Rudolph W. Giuliani to push Ukraine into investigating the Bidens and 2016 election interference.

Republicans said Mr. Taylor’s testimony was “contradicted” by other witnesses who said there was no quid pro quo.

“Much of what Mr. Taylor said yesterday was second- and third-hand information,” said House Majority Leader Kevin McCarthy, California Republican.

In the wake of Mr. Taylor’s testimony, the committees leading the impeachment probe issued a new demand for State Department documents, including text messages from witnesses and any memos regarding efforts to press Ukraine to open investigations.

Meanwhile, three Democratic senators filed a Freedom of Information Act request with the Justice Department for documents related to Ukraine.

And a federal judge ordered the State Department to begin releasing Ukraine-related documents within 30 days. Those documents include communications between Mr. Giuliani and Secretary of State Mike Pompeo.

U.S. District Judge Christopher Cooper, an Obama appointee, issued the ruling in response to a Freedom of Information Act request by American Oversight, a left-leaning government watchdog organization.

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