A day after Hillary Clinton tried to clear the air over her extensive use of personal email while secretary of state, the picture became muddied again as Republicans cited her decision to delete thousands of emails and lock down her server in questioning whether she was being truly transparent.

Congressional investigators are now focusing on that server and looking to pressure her into turning it over -- despite her insistence Tuesday that "the server will remain private."

Rep. Trey Gowdy, R-S.C., head of the House committee investigating the 2012 Benghazi attacks, said in a statement that without access to it, "there is no way for the State Department to know it has acquired all documents that should be made public."

He said he sees "no choice" but for Clinton to turn over the server "to a neutral, detached third-party arbiter who can determine which documents should be public and which should remain private."

The former secretary of state showed no interest in doing so during her press conference.

She said she has "more than met" the State Department's request for records, and the server "contains personal communications from my husband and me." Clinton said that will remain "private."

She also said her personal emails, which she didn't keep and didn't turn over, covered everything from her daughter Chelsea's wedding to yoga routines.

Speaking with Fox News' "On the Record with Greta Van Susteren," Gowdy said: "I have no interest in her yoga routine, trust me. I have no interest in that. But I have every interest in public record, whether it's related to Libya or not, and I have no interest in her personal attorney determining what is a public record and what is not a public record.

"That should be done by a neutral, detached person."

Despite some questions over the actual location of the server, Clinton's office released a statement on Tuesday clarifying that it was "physically located on her property, which is protected by U.S. Secret Service."

But even if Clinton could be convinced -- or compelled -- to turn over the server, it's unclear what investigators might be able to find. Her office said in its written statement that she "chose not to keep" thousands of "private, personal emails" that were described as "not federal records."

Specifically, her office said that includes 31,830 emails. Another 30,490 "work-related" emails were turned over to the State Department.

The question is whether those private emails might be recoverable so a "third party" could review them. Republicans suggest Clinton should not be the one who decides what is a personal and what is a work-related message.

"Because only Hillary Clinton controls her personal email account and admitted she deleted many of her emails, no one but Hillary Clinton knows if she handed over every relevant email," Republican National Committee Chairman Reince Priebus said in a statement.

Meanwhile, Clinton's statement that her server contained personal messages between her and her husband seemed to run against a Wall Street Journal report that, quoting former President Bill Clinton's office, said the former president doesn't use email himself -- other than sending a total of two emails during his time in the White House. Neither of those emails was to his wife.