By Julia Harte

WASHINGTON (Reuters) - The top U.S. law enforcement official, under questioning from Republicans at a congressional hearing on Tuesday, shed no new light on the Justice Department's decision not to prosecute Hillary Clinton over her handling of sensitive emails.

Attorney General Loretta Lynch deflected questions about the department's inquiry into Clinton's use of a private email system while she was secretary of state, an issue that has hounded her campaign for the Democratic presidential nomination.

Republicans grilled Lynch at the House of Representatives committee hearing over Justice's decision not to charge Clinton, the presumptive Democratic nominee for the Nov. 8 election.

"Lynch has no intention of answering ... even the most basic questions about the legal elements the government is obligated to prove in a criminal prosecution," said House Judiciary Committee Chairman Bob Goodlatte, a Republican.

Democratic lawmakers at the hearing largely avoided the subject, asking Lynch about gun control and policing reforms.

Lynch referred questions about the department's decision to an FBI-led investigative team that recommended not bringing charges. She said she was "extremely proud" of the team's work, testifying one week after the FBI closed its year-long probe.

The emails case is a favorite target for presumptive Republican presidential nominee Donald Trump, as well as other Republican politicians.

Goodlatte and Republican Representative Jason Chaffetz asked the Justice Department on Monday to investigate whether Clinton committed perjury in testimony to Congress about the emails.

Other investigations continue. At least one federal judge is seeking to establish whether Clinton set up the email system to thwart laws governing the public's access to official records. Judge Emmet Sullivan of the district court in Washington, who is overseeing a lawsuit accusing the State Department of not complying with records requests by the conservative watchdog group Judicial Watch, is considering whether to order that Clinton give testimony about the system under oath.

Clinton's lawyers argued against her having to testify in court papers filed on Tuesday, saying she had no more information to provide that was not already in the public record and that the Justice Department still had her emails and computer equipment. Judge Sullivan is due to rule on whether to order the deposition after a hearing next Monday.

FBI Director James Comey told a congressional hearing last week he recommended against charging Clinton because there was insufficient evidence that she acted with bad intent. He added that any of his employees who handled emails the way Clinton did could be subject to dismissal or loss of security clearance.

(Reporting by Julia Harte; Additional reporting by Jonathan Allen; Editing by James Dalgleish and Kevin Drawbaugh)