The whistleblower who sparked the impeachment inquiry into Donald Trump will not testify in public, the House intelligence chair, Adam Schiff, said.

“The committee … will not facilitate efforts by President Trump and his allies in Congress to threaten, intimidate and retaliate against the whistleblower who courageously raised the initial alarm,” Schiff said in a letter to the ranking Republican, Devin Nunes, released on Saturday night.

It comes as an associate of Rudolph Giuliani said he travelled to Ukraine to warn that unless an investigation was announced into Joe Biden and his son, Hunter, US aid would be frozen to the country and Mike Pence would not attend the swearing-in of the new president.

According to the New York Times, the claim by Lev Parnas, a Soviet-born American charged last month with campaign finance violations for channelling foreign money into the president’s campaign, “directly links” Giuliani, Trump’s personal lawyer, to threats of repercussions or a quid pro quo with Ukraine, which is at the heart of the impeachment inquiry.

House investigations centre on concerns over Trump’s attempts to have Ukraine investigate his political rivals, in return for nearly $400m in military aid and a White House visit for President Volodymyr Zelenskiy.

Parnas is preparing to speak to impeachment investigators but his account has been disputed by his business partner, Igor Fruman, who was also charged with campaign finance violations, and by Giuliani, who told the NYT he “categorically” did not tell Parnas to deliver the reported message to Ukraine.

The impeachment inquiry followed the whistleblower, an intelligence official, raising concerns about a 25 July phone call between Trump and Zelenskiy in which the US president raised the notion of his counterpart doing the US “a favour”. The incomplete White House memo about the 25 July call remains a key point of contention. Trump said on Saturday he would soon release details of another call with the Ukrainian leader.

House committees led by Schiff have so far heard testimony in private. Transcripts released this week were mostly damaging to the White House, bringing the acting chief of staff, Mick Mulvaney, firmly into the spotlight over his apparent role in offering the quid pro quo.

Mulvaney and other key aides have refused to testify, defying congressional subpoenas and raising fears of a constitutional crisis. On Friday night, Mulvaney asked to join a lawsuit which asks a judge to decide whether a more junior aide should testify. The move could put the chief of staff at odds with the president he serves.

This is a very simple, straightforward act: the president broke the law Jackie Speier

Public hearings are scheduled to begin on Wednesday.

In his own letter on Saturday, Nunes criticised Schiff’s handling of the impeachment inquiry and set out the witnesses Republicans would like to question.

Among them were the whistleblower, whom the president and his allies have demanded be identified contrary to federal law; Hunter Biden, the son of former vice-president Joe Biden who is accused without evidence of corruption in Ukraine; Alexandra Chalupa, a Ukrainian-American former Democratic National Committee staffer; and Nellie Ohr, a former contractor for the political intelligence firm Fusion GPS, which commissioned the famous Steele dossier on Russian election interference and links between Trump and Moscow.

The move indicated a key Republican tactic: to steer argument towards supposed wrongdoing regarding Ukraine involving Trump’s enemies, not the president.

Schiff countered, saying the inquiry and his committee would “not serve as vehicles” for “sham investigations into the Bidens or debunked conspiracies about 2016 US election interference that President Trump pressed Ukraine to conduct for his personal political benefit”.

On Fox News’ Sunday Morning Futures With Maria Bartiromo, the Trump ally and South Carolina senator Lindsey Graham trafficked in one such conspiracy theory, saying: “When you find out who the whistleblower is you will find out it’s somebody from the Deep State and had interactions with Schiff and this thing’s going to stink to high heaven.”

The Deep State conspiracy theory holds that a permanent and unelected government of bureaucrats and security officials is determined to thwart Trump. In a recent book by the New York Times reporter James B Stewart, the former White House adviser Steve Bannon, a key propagator of the theory, said it was “for nut cases”.

Public hearings will bring the inquiry on to the national stage, opening a vital front in the battle for public opinion as an election year looms. Successive polls have shown slim majorities backing Trump’s impeachment and removal. As Democrats hold the House, it seems likely it will vote for impeachment. As Republicans hold the Senate, it seems unlikely Trump will be convicted and removed.

On Sunday members of key House committees set out the parties’ positions on why Trump is being impeached, cases they must now take to the American people.

On CBS’s Face the Nation, Eric Swalwell, a California Democrat on the intelligence committee, said: “We have evidence of an extortion scheme using taxpayer dollars to ask a foreign government to investigate the president’s opponent.”

On ABC’s This Week, Jackie Speier, also a California Democrat and a member of the intelligence panel, boiled it down further: “This is a very simple, straightforward act: the president broke the law.”

For the Republicans, the House armed services committee ranking member, Mac Thornberry, told ABC of Trump’s behaviour: “I believe it was inappropriate, I do not believe it was impeachable.”

Thornberry also repeated a common charge from Republicans – made by Trump on Twitter – that Democrats running the inquiry are doing so in partisan fashion.

“There has to be a fair way to arbitrate,” he said, “to decide who the witnesses are. We have had none of that so far.”

Democrats have countered that they are following rules laid down by Republicans when they investigated Hillary Clinton over the Benghazi attack of September 2012.

Two Republican senators insisted Trump had done nothing wrong. On CNN’s State of the Union, Ron Johnson of Wisconsin said Trump had not sought a quid pro quo.

“I’ve never heard the president say, ‘I want to dig up dirt on a potential 2020 opponent,’” Johnson said. “What I’ve always heard the president consistently concerned about is ‘what happened in 2016. How did this false narrative with Russian collusion with my campaign occur? Why was I strapped with the special counsel?’ It’s a very human desire.”

On NBC’s Meet the Press, the libertarian Kentuckian Rand Paul indicated that Trump did seek a quid pro quo, and said doing so was not wrong.

“I think it’s a big mistake for anybody to argue ‘Quid pro quo, he didn’t have quid pro quo,’” Paul said. “And I know that’s what the administration’s arguing. I wouldn’t make that argument.

“I would make the argument that every politician in Washington, other than me, virtually, is trying to manipulate Ukraine to their purposes.”