(CNN) The lawyer for embattled FBI agent Peter Strzok slammed House Republicans for selectively leaking portions of Strzok's closed-door testimony last week and charged that the invitation for Strzok to return next week for a public grilling was a "trap."

The attorney, Aitan Goelman, sent the House Judiciary Committee a blistering letter, obtained by CNN, that accused Republicans of forcing Strzok to testify behind closed doors when he wanted to testify publicly and then twisting his answers to the media.

Following his closed-door interview last week, the committee invited Strzok to return to testify publicly on July 10, but Goelman said that date would not work — and raised the possibility he would not return to speak with the panel at all.

"Having sharpened their knives behind closed doors, the committee would now like to drag back Special Agent Strzok and have him testify in public — a request that we originally made and the committee denied," Goelman said. "What's being asked of Special Agent Strzok is to participate in what anyone can recognize as a trap."

Strzok's attorney also called for the transcript of last week's interview, which spanned more than 11 hours, to be released. It's unclear whether Strzok will accept an invitation to testify unless the transcript is publicly released, according to a source familiar with the negotiations.

The letter from Strzok's attorney is the latest shot in the battle between House Republicans and the Justice Department and FBI over the handling of investigations into Hillary Clinton's private email and possible collusion between Donald Trump's team and Russia.

Strzok has been vilified by Republicans for the anti-Trump text messages he exchanged with FBI lawyer Lisa Page. Strzok and Page, who were having an extramarital affair, worked on the Hillary Clinton and Russia investigations and were part of special counsel Robert Mueller's initial team. Strzok was removed from Mueller's team when the messages were discovered, but Trump and his allies have argued the text messages show Mueller's probe is biased.

The House Judiciary Committee is not the only committee that's seeking Strzok's testimony. Rep. Adam Schiff, the top Democrat on the House Intelligence Committee, invited Strzok to appear last month as part of the Democrats' continuation of the panel's Russia investigation. And several Senate committees would also like to speak with him.

In the letter, Goelman raised the prospect that Strzok might testify in front of another committee.

"Given that the committee is playing political games, violating our trust and its own rules, it no longer makes sense for us to keep playing along," he wrote. "(Strzok) is willing to testify again, and he is willing to testify publicly. ... He might even be willing to testify publicly before this committee. But not under conditions that are so obviously designed to embarrass and a trap an honorable man who has spent 25 years serving his country in the military and in law enforcement."

A spokeswoman for House Judiciary Chairman Bob Goodlatte did not respond to a request for comment.

Strzok's closed-door testimony was raised at several points during the committee's hearing last week with Deputy Attorney General Rod Rosenstein, which began roughly 12 hours after Strzok left the Capitol complex the night before.

Republicans expressed frustration that Strzok was instructed by FBI counsel not to answer questions related to the Russia investigation and other matters.

"Why'd you tell Peter Strzok not to answer our questions yesterday?" Rep. Jim Jordan of Ohio asked Rosenstein, who responded that he gave Strzok no instructions. "When I asked Peter Strzok if he'd ever communicated with Glenn Simpson, he gave us the answer he gave us dozens of times: 'On advice of FBI counsel, I can't answer that question,'" Jordan continued.

Rep. John Ratcliffe of Texas said at the hearing Strzok had testified that when Mueller dismissed him over the anti-Trump text messages, Mueller did not ask Strzok whether the bias found in the text messages influenced his actions.

Democrats objected that Republicans were citing the testimony that was not public.

"We had a closed hearing on Peter Strzok. If you want to color his testimony like this, release the transcript," said Rep. Ted Lieu of California. "Have an open hearing. Don't characterize and not let him testify."

In his letter to the committee, Goelman wrote that Republican lawmakers "rushed to the media to mischaracterize Special Agent Strzok's testimony, calling him a liar and telling reporters he refused to answer many questions on the advice of counsel."

Goelman said that wasn't true, because Strzok, who is still an FBI employee, was instructed by the bureau that he could not answer questions about the Russia investigation. The attorney suggested the committee and the FBI should work out an arrangement on that issue before Strzok returns.

The letter also accused Republicans of asking unserious questions during the interview and cutting him off before he could respond.

It cited several of the questions asked, including: "What DO Trump supporters SMELL like, agent?", "Did you love Lisa Page?" and "Which party primary did you vote in in 2016?" Strzok told lawmakers he is not affiliated with a political party, Goelman said.