Hillary Clinton's private email server should be examined by the U.S. intelligence watchdog after the FBI finishes reviewing any classified information on it, a Republican lawmaker said on Sunday.

The FBI recently began looking into the security of federal records and possible classified information among the Democratic presidential candidate's emails while she was secretary of state.

After months of pressure, Clinton last week gave the FBI her private email server and a thumb drive of work-related emails from her tenure.

Trey Gowdy, chair of a U.S. House of Representatives committee investigating the killing of four Americans at a U.S. diplomatic building in Benghazi, said there should also be a probe into whether Clinton has handed over all her emails.

"When the bureau is through with the server, I hope they turn that server over to the Inspector General so they can determine whether or not the record is full and complete," Gowdy told "Fox News Sunday."

A spokesman for Clinton's presidential campaign and the FBI did not immediately respond to requests for comment.

Last December, Clinton handed over about 30,000 emails she sent and received while America's top diplomat, although her staff have since acknowledged without explanation that some work emails are missing.

Clinton made a joke of the controversy over her email on Friday at a Democratic fundraising event in Iowa, and posted a video of her comments on her Twitter account.

"You may have seen that I recently launched a Snapchat account," she said, referring to the social media company that allows users to send messages that disappear in seconds.

"I love it. I love it. Those messages disappear all by themselves," she said in the video.

(Reporting by Lindsay Dunsmuir; Editing by Tom Heneghan)