Updated at 5:11 p.m. ET

President Trump said Monday that he will "strongly consider" providing written testimony to House impeachment investigators. The president's surprise announcement comes a day after top Democrats invited him to defend himself in the face of accusations that he committed bribery by allegedly using foreign policy as a way to help his 2020 reelection bid.

"Even though I did nothing wrong, and don't like giving credibility to this No Due Process Hoax, I like the idea & will, in order to get Congress focused again, strongly consider it!" Trump tweeted.

Eight more witnesses are set to testify this week, marking the second week of public hearings examining whether the president abused his office by leveraging hundreds of millions of dollars in military assistance to push Ukraine to investigate one of Trump's chief political rivals.

Among the most anticipated scheduled witnesses is Gordon Sondland, a wealthy hotelier from Oregon who is Trump's ambassador to the European Union.

In a deposition transcript released over the weekend, it was revealed that Sondland and Trump spoke to each other about five times around the time that $391 million in security assistance to Ukraine was frozen, according to what former National Security Council aide Tim Morrison told House investigators.

Sondland is set to address House lawmakers on Wednesday.

The president and his defenders have assailed the motives and credibility of the parade of witnesses who have largely supported the complaint filed by an anonymous whistleblower that helped launch the inquiry.

On Sunday, Trump took a swipe at an aide assigned to Vice President Mike Pence's office scheduled this week to give testimony, calling her a "Never Trumper."

The same day, House Speaker Nancy Pelosi said the president can "speak all the truth that he wants" under oath in front of House investigators. At a Sunday news conference in New York, Senate Minority Leader Chuck Schumer elaborated on Pelosi's offer.

"If Donald Trump doesn't agree with what he's hearing, doesn't like what he's hearing, he shouldn't tweet — he should come to the committee and testify under oath. And he should allow all those around him to come to the committee and testify under oath," Schumer said.

Trump declined to testify in person when Robert Mueller was investigating the Trump campaign and Russian election interference in the 2016 election, but he did submit written testimony.

House impeachment investigators are now trying to determine whether the president lied in those written answers, Doug Letter, general counsel for the House of Representatives, confirmed to NPR on Monday.

Letter first indicated that the Democratic-controlled Judiciary Committee was interested in exploring whether Trump lied in his written deposition to Mueller in a September court filing as part of a case in which Democrats are seeking secret grand jury testimony from Mueller's probe.

"Not only could those materials demonstrate the President's motives for obstructing the Special Counsel's investigation, they also could reveal that Trump was aware of his campaign's contacts with WikiLeaks bearing on whether the President was untruthful, and further obstructed the Special Counsel's investigation, when in providing written responses to the Special Counsel's questions he denied being aware of any communications between his campaign and WikiLeaks," Letter wrote in a filing to Washington's U.S. District Court on Sept. 30.

A judge ordered that the Mueller material Democrats sought be released, but the Department of Justice appealed. The two sides met on Monday for oral arguments in front of a federal appeals court, which has not yet ruled on the case.

While Trump appeared to be warming to the idea of sharing written testimony for the impeachment inquiry, he had dismissed the format as insufficient when it was offered by a person who has been the target of Trump ire: the whistleblower who filed the complaint that kicked off the impeachment inquiry.

Earlier this month, Trump tweeted "written answers not acceptable!" after the legal team representing the whistleblower, who filed the complaint over the July 25 call between Trump and the Ukrainian president, said the whistleblower would respond to written questions under penalty of perjury. But House Republicans ignored the offer.

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