Washington (CNN) As lawmakers from six committees continue to sift through a new trove of text messages from top FBI officials Peter Strzok and Lisa Page, details of what one GOP senator called their "jaw-dropping" exchanges are trickling out.

In one, Strzok, the former No. 2 counterintelligence official at the FBI, seemed to suggest he didn't think there was any "'there' there" to the special counsel investigation into Russian interference in the US election, according to Sen. Ron Johnson, the chairman of the Senate Homeland Security Committee.

In others, the pair discussed "our task" and a "secret society," as well as ways to "fix" damage done by the FBI's investigation into Hillary Clinton's email server, Johnson and House Oversight Committee Chairman Trey Gowdy said.

"That is a level of bias that is stunning among law enforcement officers," Gowdy said Tuesday on Fox News. "It is manifest bias not just against Trump, but against his kids, against his business interests."

The revelations from the new trove of text messages come at the same time as leading Republicans have quizzed the FBI over a missing series of exchanges between the two officials , with some Republicans suggesting there could be a nefarious motive behind the gap.

President Donald Trump referred to the missing texts late Tuesday night, asking about the whereabouts of the "50,000 important text messages." That figure, however, refers to the total number of texts between Strzok and Page that the Justice Department inspector general has reviewed on FBI servers. The number of missing texts, which span a five-month period, is not known.

Attorney General Jeff Sessions promised Monday to "leave no stone unturned" in an investigation to determine how the messages, sent on bureau-issued phones, were not collected by the FBI's retention software.

On Tuesday, the Republican and Democratic lawmakers atop the Senate Intelligence Committee, which is conducting its own probe into Russian election interference, both downplayed the possibility of any wrongdoing behind the missing texts.

"I don't know that I read anything into it other than that there may be a technical glitch at the bureau," Sen. Richard Burr, the Republican chairman, told CNN's Manu Raju. "The fact that they have provided the rest of them certainly doesn't show an intent to try to withhold anything. We've just got to wait until we find out."

Added the committee's top Democrat, Sen. Mark Warner: "At this point I accept the FBI's word."

In a cover letter accompanying the delivery of the messages, Assistant Attorney General Stephen Boyd explained that technical issues with the FBI's retention software prevented the bureau from capturing messages sent between the two employees on their agency-issued Samsung 5 phones from December 14, 2016 to May 17, 2017.

The Republican chairmen of the Senate Judiciary Committee and Senate Homeland Security Committee also Tuesday sent a letter to the Justice Department's inspector general requesting more information on the missing texts.

In the letter, Sens. Chuck Grassley and Johnson wrote that the IG told them last month that the IG's office had received all text messages between Strzok and Page from November 30, 2016 to July 28, 2017, contradicting the gap reported in the cover letter.

"These statements ... need to be reconciled," the senators wrote.

House and Senate investigators Tuesday were still going through 384 pages of text messages. They were turned over Friday evening by the Justice Department, and follow a separate production last month that included insults flung by Strzok and Page at members of both parties.

Their texting history, which Sessions said included over 50,000 messages outside of the uncollected period, is currently under review by the Justice Department's inspector general, who is conducting a separate probe of the FBI's handling of the Clinton email investigation.

Strzok and Page both served briefly on special counsel Robert Mueller's investigation into Russian interference in the 2016 US election. Strzok, who also helped launch the Clinton probe, was reassigned to the FBI's human resources office after the discovery of the messages. Page completed her detail with Mueller's team before the special counsel's office was made aware of the texts.

In a radio interview Tuesday morning, Johnson read two new exchanges that he called "jaw-dropping."

On May 19, two days after the appointment of Mueller, Strzok and Page were "talking back and forth about their futures at the FBI and the recent appointment of Mueller and they're talking about what they ought to do," Johnson said, "and it indicates that they're considering joining that Mueller special counsel investigation. Strzok says 'You and I both know the odds are nothing. If I thought it was likely I'd be there no question. I hesitate in part because of my gut sense and concern, there's no big 'there' there.'"

"He doesn't know if he really wants to join (the Mueller team) because his gut sense is there's no big 'there,' there. I think that's kind of jaw-dropping," Johnson told WISN 1130.

Despite Johnson's characterization, it is not immediately clear what Strzok is referring to with his "'there,' there" comment, based on a fuller exchange of the May 19 texts released later Tuesday by Johnson's office. CNN has reached out to a representative for Strzok for clarification and has not yet received a response. The FBI declined to comment to CNN for this report.

The more complete copy of the exchange shows Page appearing to discourage Strzok from joining the Mueller team.

"Why not, re me?" Strzok replies. "An investigation leading to impeachment?"

Earlier in the back and forth, Strzok writes, "I personally have a sense of unfinished business. [Redacted] unleashed it with MYE. Now i [sic] need to fix it and finish it," MYE is an apparent reference to "Midyear Exam" -- the FBI's internal case name for the Clinton investigation.

In the radio interview Johnson also read another text, sent from Page to Strzok on November 14, 2016, eight days after the 2016 US election: "God, being here makes me angry. Lots of highfalutin national security talk. Meanwhile we have our task ahead of us."

The words "our" were capitalized, Johnson said.

"These are texts between two people holding an extramarital affair and they are completely unguarded in their communication, and so we're getting an insight into exactly what's happening inside the FBI at the highest levels," Johnson said. Multiple officials briefed on the text messages have confirmed to CNN that the pair was having an affair, helping to explain the large volume of the exchanges.

On Fox News Monday night, Gowdy divulged more details from the messages, including one text, sent the day after the election, discussing a "secret society."

"The day after the election, the day after what they really, really didn't want to have happen, there's a text exchange between these two FBI agents, these supposed to be objective, fact-centric FBI agents, saying perhaps this is the first meeting of the secret society," Gowdy said. "So, of course I'm going to want to know what secret society are you talking about because you're supposed to be investigating objectively the person who just won the electoral college."

He added, "What (Rep. John Ratcliffe, R-Texas) and I saw today was a text about not keeping texts, we saw more manifest bias against President Trump all the way through the election into the transition and I saw an interesting text that Director (James) Comey was going to update the President of the United States about an investigation. I don't know if it was the Hillary Clinton investigation because remember that had been reopened in the fall of 2016 or whether it was the Trump investigation. I just find it interesting the head of the FBI was going to update the President of the United States who at that point would have been President Obama."

A trio of top Democrats in the House Tuesday pushed back on the Republican aspersions of the FBI, saying they were done in "desperation" and "directly at odds with the facts."

"Republicans condemn FBI officials for supposedly taking action during the presidential campaign to assist Clinton and harm Trump, but this ignores the plain reality that these same FBI officials were involved in notifying Congress just days before the election that the FBI was reopening the Clinton investigation—an unprecedented action that severely damaged Clinton's bid for President," House Judiciary Committee Top Democrat Jerry Nadler, House Oversight Committee Top Democrat Elijah Cummings, and House Intelligence Committee top Democrat Adam Schiff said.