FILE - President Donald Trump speaks as he meets with sheriffs from across the country on the South Lawn of the White House in Washington, Sept. 26, 2019.
FILE - President Donald Trump speaks as he meets with sheriffs from across the country on the South Lawn of the White House in Washington, Sept. 26, 2019.

Democrats in the U.S. House of Representatives are moving ahead with their impeachment inquiry against President Donald Trump with subpoenas requesting documents from his personal lawyer and his secretary of state, as well as hearings scheduled this week with former officials involved in U.S.-Ukraine policy.

The heads of the House foreign affairs, intelligence and oversight committees have given Secretary of State Mike Pompeo until Thursday to produce documents linked to the probe launched after a whistleblower filed a complaint expressing concern Trump was "using the power of his office to solicit interference from a foreign country in the 2020 U.S. election."

WATCH: Impeachment inquiry continues

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Chairmen Eliot Engel, Adam Schiff and Elijah Cummings also issued a subpoena Monday for Trump lawyer Rudy Giuliani with an October 15 deadline.

"A growing public record, including your own statements, indicates that the President, you, and others appear to have pressed the Ukrainian government to pursue two politically-motivated investigations," the lawmakers wrote.  "The first is a prosecution of Ukrainians who provided evidence against Mr. Trump's convicted campaign chairman, Paul Manafort. The second relates to former Vice President Joseph R. Biden Jr., who is challenging President Trump for the presidency in 2020."

They demanded text messages, phone records and other communications "indicating that you were not acting alone and that other Trump Administration officials may have been involved in this scheme."

Giuliani wrote on Twitter that he had received the subpoena and would give it "appropriate consideration."

FILE - President Donald Trump's lawyer Rudy Giuliani speaks to reporter's on the South Lawn of the White House in Washington, May 30, 2018.

"It raises significant issues concerning legitimacy and constitutional and legal issues including, inter alia, attorney client and other privileges," he said.

Giuliani has criticized Democrats as having "no basis for impeachment" and sought to bring focus to his allegations of wrongdoing against Biden.

The whistleblower alleges that Trump sought Ukrainian President Volodymyr Zelenskiy's help in digging up incriminating information about Biden and his son Hunter that would hurt Biden's prospects of winning the Democratic presidential nomination and challenging Trump in next year's vote.

Trump reiterated his defense Monday that his July 25 phone call with Zelenskiy "was perfect."

The president says he wants to meet the whistleblower, and expressed Monday a desire to know more about them.

"Well, we're trying to find out about a whistleblower," he told reporters when asked if he knew the person's identity.

Lawyers representing the whistleblower have expressed concerns for the individual's safety and stressed the need to keep their identity secret.

"The Intel Community Whistleblower is entitled to anonymity. Law and policy support this and the individual is not to be retaliated against.  Doing so is a violation of federal law," lead attorney Andrew Bakaj said Monday.

Trump has also seized on the way Schiff portrayed the July phone call during a hearing last week.  Schiff said the transcript released by the White House "reads like a classic organized crime shakedown" and paraphrased Trump's words in a parody fashion.

"When the whistleblower reported it, he made it sound terrible," Trump told reporters Monday.  "And then, you had Adam Schiff who, even worse, made up my words, which I think is just horrible.  I've never seen a thing like that."

He also used Twitter to suggest Schiff face severe punishment.

"Rep. Adam Schiff illegally made up a FAKE & terrible statement, pretended it to be mine as the most important part of my call to the Ukrainian President, and read it aloud to Congress and the American people. It bore NO relationship to what I said on the call. Arrest for Treason?" Trump wrote.

Wednesday brings a House hearing featuring testimony from Marie Yovanovitch, who was the U.S. ambassador to Ukraine before Trump removed her earlier this year.  On Thursday, lawmakers will hear from Kurt Volker, who resigned his post as U.S. envoy to Ukraine last week.