But Mr. Ryan would not say if he supported the effort of House Intelligence Committee Chairman Devin Nunes, California Republican, to hold Attorney General Jeff Sessions in contempt if the documents are not given to Congress.
Nunes has requested and filed a subpoena for heavily classified documents that relate to Mueller's probe.
The Washington Post reported Tuesday that the Federal Bureau of Investigation and national intelligence officials warned the White House last week that information requested by Nunes could put a confidential United States intelligence source at risk, but Nunes and other House Republicans have since claimed that his document request did not refer to a specific individual.
According to the Post, intelligence officials are hesitant to share even a redacted version of the document for fear it could expose the source.
In a statement after their meeting, Nunes and Gowdy said that they had a "productive discussion" with FBI, DOJ and Office of the Director of National Intelligence officials and that the officials "committed to holding further discussions of these matters" next week.
Justice Department spokeswoman Sarah Isgur Flores told HuffPost that Nunes and Gowdy ― as well as Rep. Adam Schiff (D-Calif.), ranking member on the intelligence committee ― had been invited to department headquarters to discuss the matter on Thursday.
The lawmakers are seeking documents related to special counsel Robert Mueller's investigation into the Trump campaign's ties to Russian Federation.
Nunes, in turn, has become increasingly agitated, publicly claiming that the Justice Department is attempting to "evade congressional oversight while leaking information to The Washington Post ostensibly about classified meetings".
"I think that the Department of Justice and Chairman Nunes should be having more conversations about sharing more information", said Marc Short, head of legislative affairs for the White House.
In a statement released Thursday afternoon, Nunes and Gowdy said they had a "productive" meeting with officials from the Justice Department, the Federal Bureau of Investigation and the Office of the Director of National Intelligence. "This request is perfectly appropriate within the scope of the committee's investigation, and I hope and believe and expect that they'll be complied with". Nunes has repeatedly challenged the accuracy of applications the department made to conduct surveillance on Carter Page, a former Trump campaign adviser who had contacts with Russians that the Federal Bureau of Investigation deemed suspicious.
The debate over the risk to the source is now at the center of a pitched battle between House Republicans and the Justice Department.
Top White House officials, with the assent of President Donald Trump, agreed to back the decision to withhold the information. Deputy Attorney General Rod Rosenstein and Mr. Nunes discussed the matter over the phone Tuesday, according to a CNN report.