Mr Trump's leading US presidential rival.
Bill Taylor, the top US diplomat in Ukraine, told impeachment hearings he had a "clear understanding" aid would be withheld pending an investigation.
Mr Trump denies any abuse of power.
Public impeachment hearings will begin next Wednesday, with Mr Taylor set to be the first witness called.
Mr Taylor testified in a closed-door impeachment hearing last month, and a transcript of his evidence was released to the public on Wednesday.
He told a congressional committee that two state department officials said Mr Trump would not "sign a cheque" for nearly $400m (£311m) in US military aid until Ukrainian officials announced an investigation into Democratic presidential contender and former US Vice-President Joe Biden.
Mr Biden's son Hunter previously sat on the board of the Ukrainian oil company Burisma. President Trump has claimed without evidence that Joe Biden used his position as vice-president to quash an investigation into Burisma.
Mr Taylor stopped short of directly implicating Mr Trump.
He said that the president's personal lawyer, Rudy Giuliani, was behind the drive to get Ukraine to announce an investigation into the Bidens.
Asked if the president was directing these activities, he replied: "I don't know."
However, Mr Taylor said he had also been told by Gordon Sondland, the US envoy to the EU, that Mr Trump "was adamant" Ukraine's president must personally announce an investigation into Burisma.
Mr Taylor's evidence prompted Mr Sondland this week to change his own story.
Mr Sondland had initially testified there were no preconditions to the US military aid.
But following Mr Taylor's testimony he provided a letter through his lawyer to the committee saying that he now remembered telling a Ukrainian official that US aid "likely" hinged on the Ukrainians agreeing to announce the corruption investigation requested by Mr Trump.
Mr Trump denies using US aid as a bargaining chip to target a domestic political rival.
Also on Thursday, US media reported that Mr Trump had asked the attorney general, William Barr, to hold a news conference to declare that the president had broken no laws during his July call with the Ukrainian president. This phone call triggered a whistleblower's complaint against Mr Trump and the subsequent impeachment inquiry.
Mr Barr, a Trump appointee who has proven a staunch ally of the president, reportedly refused to do so. Mr Trump denied it.
House Intelligence Committee chairman Adam Schiff, who is overseeing the inquiry, told reporters on Wednesday that the evidence for presidential wrongdoing was growing.
He said: "We are getting an increasing appreciation for just what took place during the course of the last year - and the degree to which the president enlisted whole departments of government in the illicit aim to get Ukraine to dig up dirt on a political opponent."
Next week's Capitol Hill impeachment hearings will be broadcast live, with both Democratic and Republican lawmakers questioning witnesses.
The transcript in black and white
By Jon Sopel, BBC North America editor
Seeing it in black and white lays it out very clearly. The US military aid - plus a visit to the White House for the Ukrainian president - was the prize. But there would be no prize if the Ukrainians did not announce an investigation into the Bidens.
The other thing you get from this transcript is the sense of shock that seasoned officials like Bill Taylor had, this sense that all normal rules had been suspended, that these dealings were all going through a side channel led by the president's personal lawyer Rudy Giuliani, and the State Department was playing no role in it.
Then you see Taylor's utter astonishment at the idea that military aid - aid vital to the Ukrainians - was going to be withheld, out of the blue. He's on a call and suddenly he hears, "We're stopping it". The transcript of his evidence is shocking, and it sets the stage for blockbuster hearings next week.
Quick facts on impeachment
Impeachment is the first part - the charges - of a two-stage political process by which Congress can remove a president from office. If, following the hearings, the House of Representatives votes to pass articles of impeachment, the Senate is forced to hold a trial.
A Senate vote requires a two-thirds majority to convict and remove the president - unlikely in this case, given that Mr Trump's party controls the chamber.
Only two US presidents in history - Bill Clinton and Andrew Johnson - have been impeached, but neither was convicted. President Richard Nixon resigned before he could be impeached.