Washington(CNN) The US House of Representatives may be considering articles of impeachment against President Donald Trump that go further than the Ukraine issue, including obstruction of justice and interference with federal elections accusations, the top House lawyer said in federal court Tuesday.

"I can't emphasize enough, it's not just Ukraine," House General Counsel Doug Letter told Chief Judge Beryl Howell of the US District Court in Washington, DC.

Letter said Trump could be impeached for lying to the American public.

Howell asked if Trump had to have committed a crime to be impeached. The answer from Letter was an unequivocal "no."

Howell then asked if Trump could be impeached for lying to the American public. "I believe so, yes," Letter said.

"Another possible impeachment count is obstruction of Congress," Letter added.

A hypothetical Senate conviction of the President following a House impeachment inquiry wouldn't need to stick to criminal legal issues, Letter said.

The court hearing Tuesday morning covered many of the legal questions that the House and White House are fighting over this week as the Ukraine impeachment inquiry moves forward. The hearing was set to focus on grand jury secrets in the report by special counsel Robert Mueller, but Howell has asked several pointed questions about the parameters of the current impeachment probe.

Fight over FBI memos from Mueller probe

The House is trying to obtain FBI memos on what then-White House counsel Don McGahn and other White House employees told former Mueller about the President's activity that prompted questions about attempts to obstruct justice. The Justice Department has refused to share those documents, Letter said.

"We're getting almost nothing," he said.

The House has seen no FBI interview notes (so-called 302s) from McGahn, his then-deputy Annie Donaldson or of others in the White House, despite saying they need them and the Justice Department agreeing to share some of the memos with the House.

The Justice Department said Tuesday that it has agreed to give the House 33 FBI memos from the Mueller investigation for use in the impeachment inquiry. But the documents have redactions "to protect confidential communications between senior White House advisers," Justice Department attorney Elizabeth Shapiro said.

Howell responded with incredulity, pointing out that the White House appeared to be keeping confidential from the House information that was widely available within the FBI. Shapiro responded that it was not widely shared within the FBI.

Does House have to vote on impeachment inquiry?

The White House and congressional Republicans say the House needs to vote to formally begin an impeachment inquiry, a move House Speaker Nancy Pelosi has avoided and says is unnecessary.

"The House sets its own rules" and "has sole power over impeachment," Letter said, adding that the federal courts should allow the House to have whatever it needs, citing a previous legal opinion.

This story is breaking and will be updated.