Senator Mitch McConnell appeared to put to rest speculation that he would use his position to derail any impeachment effort by the Democratic-led House by avoiding a trial at all.
In issuing a separate subpoena last week as part of the inquiry, the chairmen of three House committees made it clear that stonewalling their investigation would be considered obstruction of Congress in its investigation.
The impeachment inquiry could lead to approval of articles of impeachment - or formal charges - against Trump in the House.
"I would have no choice but to take it up", Mr McConnell told CNBC.
Appearing on "America's Newsroom" with host Sandra Smith, Gingrich said that the Democrats' impeachment inquiry was "a purely political process". Prior to the call, Trump had suspended $400m in USA security assistance to Ukraine, prompting speculation that the president was holding out on the money pending the outcome of his conversation with the new president. Zelenskiy in the call agreed to investigate.
A spokesman for Mr Schiff did not respond to a request for comment on the remarks.
Witnesses are due to testify in the House this week in hearings about Mr Trump's request that Ukraine investigate Joe Biden.
The chairmen are demanding he turn over the documents by October 15.
Schiff launched the impeachment probe on Friday after a White House summary memo of Trump's July 25 call with Zelensky supported a whistleblower's allegations that Trump tried to enlist Ukraine's help in his fight for reelection next year, and then tried to hide the fact.
The whistleblower has not been publicly identified, but Mr Trump said on Monday that "we're trying to find out about a whistleblower".
Democrats plan to meet with the whistle-blower behind closed doors soon and a second meeting with the Intelligence Community Inspector General Michael Atkinson, who first verified the whistle-blower complaint, Schiff said. In the days after, senior White House officials sought to "lock down" records of the call, signalling White House officials "understood the gravity of what had happened", the whistle-blower said. "It's just not part of whistleblower protection law or any agency policy". The aid was later provided.
Earlier on Tuesday, Trump tweeted again about wanting to know the whistleblower's identity, asking, "Why aren't we entitled to interview & learn everything about the Whistleblower, and also the person who gave all of the false information to him". The letter contained a schedule for depositions by officials including former U.S. Ambassador to Ukraine, Marie Yovanovitch, who was abruptly recalled from her posting.
The officials "may not attend any interview or deposition" without executive branch counsel present to control disclosure of confidential information and questioned, Pompeo wrote in a letter to House Foreign Affairs Committee Chairman Eliot Engel.
The secretary of state was also served with a subpoena by House Democrats last week.