A day after a lawyer for the whistleblower who raised alarms about Donald Trump’s dealings with Ukraine said his client is willing to answer written questions submitted by House Republicans, the president tweeted: “Written answers not acceptable!”

The surprise offer to Devin Nunes, the top Republican on the House intelligence committee, would allow Republicans to ask questions of the whistleblower who spurred the Democratic-led impeachment inquiry, without having to go through the committee chairman, Adam Schiff.

The whistleblower raised concerns about Trump’s 25 July call with the Ukrainian president, Volodymyr Zelenskiy, in which Trump pressed Zelenskiy to investigate his political rivals. That call became the catalyst for the impeachment inquiry.

The offer to Nunes did not please Trump, who wrote in a familiar vein: “The whistleblower gave false information & dealt with corrupt politician Schiff. He must be brought forward to testify. Written answers not acceptable!”

During the special counsel investigation into alleged Russian meddling in the 2016 election, Trump refused to be interviewed in person and instead submitted written answers to questions from Robert Mueller.

The attorney Mark Zaid had tweeted that the whistleblower would answer questions directly from Republican members “in writing, under oath & penalty of perjury”, as part of an attempt to stem such efforts by Trump and his GOP allies to unmask the person’s identity. Only queries seeking the person’s identity would not be answered, Zaid said.

Trump’s Monday morning message continued a line of attack from the weekend. Speaking to reporters on the South Lawn of the White House on Sunday afternoon, Trump was asked if he was “thinking about tweeting out the name of the whistleblower?”

Trump replied: “Well, I’ll tell you what, there have been stories written about a certain individual, a male, and they say he’s the whistleblower. If he’s the whistleblower, he has no credibility because he’s a Brennan guy, he’s a Susan Rice guy, he’s an Obama guy and he hates Trump, and he’s a radical. Now, maybe it’s not him but, if it’s him, you guys ought to release the information.”

Zaid said: “Being a whistleblower is not a partisan job nor is impeachment an objective. That is not our role. So we have offered to Devin Nunes.

“We will ensure timely answers,” he said.

Nunes’s office did not immediately comment.

“What I said on the phone call with the Ukrainian president is ‘perfectly’ stated,” Trump also tweeted on Monday. “There is no reason to call witnesses to analyze my words and meaning. This is just another Democrat Hoax that I have had to live with from the day I got elected (and before!). Disgraceful!”

The House minority leader, Kevin McCarthy, said on Sunday he had not discussed the whistleblower’s offer with Nunes, but stressed that the person should answer questions in public appearance the committee.

“When you’re talking about the removal of the president of the United States, undoing democracy, undoing what the American public had voted for, I think that individual should come before the committee,” McCarthy told CBS’s Face the Nation.

“We need an openness that people understand this,” he said.

Republicans view a political opportunity in unmasking the CIA official, who the intelligence community’s inspector general said could have “arguable political bias”. The inspector general nevertheless found the whistleblower’s complaint to be “credible”.

Zaid said his team had addressed the issue of alleged bias with Republican members of the committee and had stressed the need for anonymity to maintain the safety of the whistleblower and that person’s family, “but with little effect in halting the attacks”.

Andrew P Bakaj, another attorney representing the whistleblower, tweeted: “Let me be absolutely clear: Our willingness to cooperate has not changed. What we object to and find offensive, however, is the effort to uncover the identity of the whistleblower.”

Bakaj wrote on Saturday that Republicans’ “fixation on exposing the whistleblower’s identity is simply because they’re at a loss as to how to address the investigations the underlying disclosure prompted”.

The whistleblower’s secondhand account of the call has been providing a road map for House Democrats investigating whether the president and others in his orbit pressured Ukraine to investigate political opponents, including former vice-president Joe Biden.

US whistleblower laws exist to protect the identity and careers of people who bring forward accusations of wrongdoing by government officials. Lawmakers in both parties have historically backed those protections.