WASHINGTON (Reuters) - Democrats in Congress, answering Republican complaints that their impeachment investigation of U.S. President Donald Trump is being conducted in secret, plan a vote on Thursday on how to make their inquiry public, a significant new stage in the probe.

Trump and his fellow Republicans have for weeks branded the work of committees probing Trump’s overtures to Ukraine as illegitimate, arguing the full Democratic-led House of Representatives had failed to authorize their investigations in a public vote.

Meeting behind closed doors, the House Intelligence, Foreign Affairs and Oversight committees have been looking into the possibility that Trump violated federal law by seeking foreign help for his November 2020 re-election efforts.

House Rules Committee Chairman James McGovern said on Monday: “I will be introducing a resolution to ensure transparency and provide a clear path forward.”

House Intelligence Committee Chairman Adam Schiff said in a statement the legislation would establish a format for open hearings.The U.S. Constitution gives the House broad authority to set ground rules for an impeachment inquiry and Democrats say they are following House rules on investigations.

Several administration officials, including a former deputy national security adviser on Monday, have failed to testify to House committees engaged in the probe.

House Speaker Nancy Pelosi said in a letter to her fellow House Democrats the House will vote this week - on Thursday, according to a senior Democratic aide - on a resolution that spells out how future public hearings will be held.

Pelosi promised to provide legal protections for Trump.

A source familiar with the probe said the public hearings will be held by the Intelligence Committee and that the transcripts from closed depositions with witnesses will be made public. A senior House Democratic aide said the hearings could begin within the next month.

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The measure will set the stage for House investigating committees to forward evidence they have collected to the House Judiciary Committee, which would then decide whether to advance articles of impeachment against Trump.

Even if the House impeaches Trump, he would face a trial in the Republican-controlled Senate, which for the moment seems unlikely to convict the president and force his ouster.

Impeachment requires a simple majority in the 435-member House but conviction demands the support of a two-thirds majority in the 100-member Senate.

WITNESS STAYS AWAY

Charles Kupperman, a former deputy to ousted national security adviser John Bolton, failed to appear earlier on Monday before the three House panels conducting the Ukraine phase of the Democratic-led impeachment inquiry, lawmakers said.

Other panels are probing separate issues, including Trump’s finances and abuses of White House security clearances.

Kupperman put off testifying while asking a court to rule on whether he should comply with a congressional subpoena or honor the Trump administration’s order not to testify, his lawyers said last week.

Democrats in turn said they would not let further legal maneuverings delay their work.

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At least nine others have testified despite being instructed by the White House not to do so, Schiff said.

Kupperman was expected to provide testimony about Trump’s dealings with Ukraine brought to Congress’ attention by a report from a whistleblower about a July 25 telephone call between the U.S. president and Ukrainian President Volodymyr Zelenskiy.

Trump’s request to Zelenskiy that he investigate former U.S. Vice President Joe Biden, a leading candidate for the 2020 Democratic presidential nomination, and his son Hunter Biden, who had served on the board of a Ukrainian gas company, is the focus of the inquiry being conducted by the three panels.

Trump made his request after withholding $391 million in security aid approved by the U.S. Congress to help fight Russian-backed separatists in eastern Ukraine.

A separate White House official, Alexander Vindman, a lieutenant colonel who sits on the National Security Council and who listened in on the call, is expected to tell lawmakers in a closed-door hearing on Tuesday that the conversation alarmed him so much that he raised concerns with an NSC lawyer.

But Trump again dismissed the inquiry in comments to reporters.

“I had a great conversation with the Ukrainian president. I had another with him also, I think before that, which was the same thing, it was nothing. They tried to take that conversation and make it into a big scandal,” Trump said on Monday.

Schiff noted that a federal judge had validated the legality of the Democratic-led impeachment inquiry in a decision about releasing information regarding a separate investigation, into Russian election interference in 2016, to Congress and that all witnesses need to come forward when called.

The Trump administration appealed that ruling on Monday.

(For a graphic on 'The impeachment inquiry' click tmsnrt.rs/30NregM)