Fed up with the lack of public access to an impeachment inquiry they likened to a “Soviet-style process,” dozens of House Republicans stormed into a closed-door Intelligence Committee hearing, refused to leave — and even ordered pizza.

The pro-Trump lawmakers, led by Rep. Matt Gaetz of Florida, barged into the Sensitive Compartmented Information Facility, where Deputy Assistant Defense Secretary Laura Cooper was preparing to give a deposition.

”Let us in!” cried the lawmakers, some of whom were carrying cellphones and other electronics in the secure location, a violation of congressional rules and, possibly, the law.

Rep. Chris Stewart (R-Utah), an Intelligence Committee member who was there for the hearing, said the GOPers didn’t know they couldn’t bring in electronics.

“There were some people that didn’t realize they couldn’t come in without their Fitbits. That was an oversight,” he told The Post.

As Cooper, a Russia and Ukraine expert, sat down to testify, the Republicans reportedly rushed through the room’s three doors shortly ­after 9 a.m.

Rep. Bradley Byrne (R-Ala.) started yelling at House Intelligence Chairman Adam Schiff, but the California Democrat did not respond and quickly left the room, located three floors below street level in the Capitol.

Other Democrats, including Rep. Val Demings of Florida, shouted back at Byrne and Rep. Louie Gohmert (R-Texas), who were yelling about the closed-door process.

“Voting members of Congress are being denied access from being able to see what’s happening behind these closed doors, where they’re trying to impeach the president of the United States with a one-sided set of rules. They call the witnesses,” declared Rep. Steve Scalise (R-La.), who later ordered Dominos pizza for reporters and New York-style pies from a shop called We the Pizza for lawmakers.

“This is a Soviet-style process. It should not be allowed in the United States of America,” Scalise went on. “Every member of Congress ought to be allowed in that room. The press ought to be allowed in that room.”

Cooper left the room while the Republicans held their sit-in, and the Capitol Police and the House sergeant at arms were brought in to end the impasse.

Democrats debated asking Capitol Police to remove the GOP protesters, but feared that would play into the Republican lawmakers’ hands, sources told The Washington Post.

The Republicans finally began leaving the Sensitive Compartmented Information Facility at about 2 p.m. for other House business, Scalise said, and the hearing resumed with Cooper by late afternoon.

President Trump this week had urged lawmakers to get tougher in fighting the impeachment inquiry against him, but Democrats slammed the tactics.

“They’re freaked out. They’re trying to stop this investigation,” Rep. Ted Lieu (D-Calif.) said.

“They don’t want to hear from witness Cooper today. They know more facts are going to be delivered which are absolutely damning to the president of the United States.”

Republican defenders of the president have called the impeachment proceedings unfair because of the lack of transparency, although closed-door hearings are far from unprecedented.

The GOP-led investigations into the terror attack in 2012 on the US embassy in Benghazi, Libya, for example, were mostly conducted behind closed doors with then-Rep. Trey Gowdy arguing that secrecy was essential to get at the truth and prevent showboating for the cameras.

In the impeachment matter, Schiff has said that the depositions have to remain confidential so that future witnesses won’t have the opportunity to coordinate their stories.

Democrats said they would eventually conduct hearings in public to present the evidence that they are gathering against the president.

Only members of the three committees conducting the probe — Intelligence, Oversight and Foreign Affairs — were authorized to be in the room.

Cooper was scheduled to testify a day after William Taylor, the top US diplomat in Ukraine, said that Trump had made nearly $400 million in military aid contingent on Ukraine President Volodymyr Zelensky publicly announcing the country would investigate Joe Biden and his son Hunter, who served on the board of a Ukrainian energy company. Trump also wanted Zelensky to announce a probe into 2016 US presidential-election interference.

Earlier Wednesday on Twitter, Trump quoted Texas GOP Rep. John Ratliffe, who disparaged Taylor’s testimony by saying: “Neither he [Taylor] or any other witness has provided testimony that the Ukrainians were aware that military aid was being withheld. You can’t have a quid pro quo with no quo.”

With Wires