Rep. Trey GowdyTrey GowdyA guide to the committees: House Congress asserts itself GOP rep says media is 'blurring' fact and opinion MORE (R-S.C.), the chairman of the House select committee investigating Benghazi, said that there is a period of missing Hillary ClintonHillary Rodham ClintonHollywood stars make political statements with Oscars fashion Live coverage: Stars get political at Oscars 5 ways politics could steal the show at Oscars MORE emails from her time as secretary of State spanning several months.
"If you think to that iconic picture of her on a C-17 flying to Libya – she has sunglasses on and she has her handheld device in her hand – we have no emails from that day. In fact, we have no emails from that trip," Gowdy said.
Clinton last week called on the State Department to publicly release the 55,000 pages of documents from her self-selected emails that she turned over for archiving.
The Republican said "it strains credibility to believe that if you're on your way to Libya to discuss Libyan policy, that there's not a single document that's been turned over to Congress" and that he has "lost confidence" in the State Department to obtain all of Clinton's emails.
Gowdy said that his committee would not yet release its store of Clinton emails "because we don't have all of them."
Gowdy's committee then issued subpoenas for all of Clinton's emails relating to the deadly 2012 attacks in Benghazi, Libya.
Rep. Adam Schiff (D-Calif.), who sits on the House Benghazi committee, pushed back against the subpoenas earlier Sunday in an interview on CNN's "State of the Union."
"They issued a subpoena for records we already have," Schiff said. "We've read them. There's nothing in them."
Gowdy suggested that his committee was keeping a tight wrap on its store of Clinton emails.
"There's a reason that serious investigations don't leak and they don't make selective releases. We had eight emails, Bob, last August. We didn't release those. We got 300 more emails totaling 800 pages in February. We haven't released those," Gowdy told host Bob Schieffer.
"It's frankly not fair to the secretary, not fair to your viewers or my fellow citizens to selectively release information. Now, if she wants to release all of them, with the emphasis being on the word all, she's welcome to do that. I can't stop her from doing it. But serious investigations don't make selective releases," he added.
Clinton has so far not directly addressed her exclusively using a private email account during her four-year tenure as secretary of State, ending in 2013.
Democrats on the committee were quick to respond Sunday, calling on Gowdy to publicly release all emails related to Benghazi instead of selectively releasing information.
"Allowing these emails to be made public will help clear up any misperceptions and will also help return the Committee to its original purpose, investigating the tragic events in Benghazi, rather than allowing it to become a surrogate for the Republican National Committee," they said in a statement sent to The Hill.
— This report was updated at 1:25 p.m.