Republican senators pressed for more information Wednesday about an FBI investigation into the potential mishandling of sensitive information that passed through former Secretary of State Hillary Clinton's private email server, and their party sued for copies of the messages.

The Republican National Committee filed two lawsuits in U.S. District Court in Washington over access to electronic messages sent or received by the Democratic presidential candidate and her top aides during her time as the nation's top diplomat.

Both spring from Freedom of Information Act requests filed last year seeking copies of emails and text messages. In court filings, the GOP says it has not received any documents in response to the requests.

The GOP litigation brings the total to at least 34 civil suits so far involving requests for federal records related to Clinton's service as secretary of state between 2009 and 2013. The Associated Press is among those with a pending case at the Washington courthouse.

"For too long the State Department has undermined the public and the media's legitimate right to records under the Freedom of Information Act, and it's time it complies with the law," said RNC Chairman Reince Priebus.

The State Department has released more than 52,000 pages of Clinton's work-related emails, but her private lawyers have withheld thousands more that they deemed to be personal communications unrelated to her job. Also left unresolved are questions about how Clinton and her closest aides handled classified information.

The AP Press last year discovered Clinton's use of the private email server, which had been set up in the basement of Clinton's New York home by former State Department staffer Bryan Pagliano, for her to use exclusively for her work-related emails while she was secretary.

The FBI for months has investigated whether sensitive information that flowed through Clinton's email server was mishandled. The State Department has acknowledged that some emails included classified information, including at the top-secret level. Clinton has said she never sent or received anything that was marked classified at the time.

The inspectors general at the State Department and for U.S. intelligence agencies are separately investigating whether rules or laws were broken.

Members of the Senate Judiciary Committee questioned Attorney General Lynch on Wednesday about media reports that the Justice Department had offered Pagliano immunity from criminal prosecution in exchange for his cooperation. Pagliano previously declined to testify before Congress, citing his Fifth Amendment rights against self-incrimination.

Sen. Chuck Grassley, the committee chairman, asked Lynch whether Pagliano's immunity offer carried over to congressional committees. Grassley, R-Iowa, wants to recall Pagliano to testify if he has received immunity.

Lynch declined to answer the question.

"We don't go into details with the agreements that we have with any witness on any matter in ongoing investigations," the attorney general said.

"The consistency with which the department handles ongoing matters, whether they involve a famous last name (or not), is something that we take very seriously," Lynch said. "We treat them the same, and that is how the public takes confidence in the investigations we conduct."

Lynch also said she had not discussed the email investigation with anyone at the White House and did not plan to do so.