House Democrats launched an impeachment inquiry against Trump on September 24 following claims by a whistle-blower that the president sought to pressure Ukraine to interfere in the 2020 presidential elections.
Mr Sondland recalled: "I said that resumption of USA aid would likely not occur until Ukraine provided the public anti-corruption statement that we had been discussing for many weeks".
Taylor also quoted himself as telling another diplomat that it would be a "nightmare" if the Trump administration withheld the military aid even if Ukraine committed to the desired investigations.
Mr. Sondland had testified on October 19 that he did not believe there was a quid pro quo for the aid to Ukraine.
Mr Sondland said he knows that proposed arrangement to be a fact because he was the one who carried the message to a Ukrainian official on the sidelines of a conference in Warsaw with vice president Mike Pence.
He was similarly disturbed by a subsequent phone call that day with Sondland, who "told me that President Trump had told him that he wants President Zelensky to state publicly that Ukraine will investigate Burisma and alleged Ukrainian interference in the 2016 US election", he said. His testimony from that deposition was released on Thursday.
"We are getting an increasing appreciation for just what took place during the course of the past year and the degree to which the president enlisted whole departments of government in the illicit aim of trying to get Ukraine to dig up dirt on a political opponent as well as further a conspiracy theory about the 2016 election that he believed would be beneficial to his re-election campaign", Intelligence Committee Chairman Adam Schiff told reporters.
"A$3 s I understood the reason for investigating Burisma was to cast Vice President Biden in a bad light", Taylor said.
The Democrats are investigating Mr Trump's requests for allegedly politically motivated probes by Ukraine as the United States withheld military aid from the country.
Congressional Democrats also released testimony from Mr Kurt Volker, Mr Trump's former special representative for Ukraine negotiations.
President Donald Trump asked that Attorney General William Barr hold a news conference clearing him of legal wrongdoing with regard to his phone call pressuring the Ukrainian President to investigate Democrats - but Barr refused, The Washington Post reported on Wednesday.
Conway also told reporters Wednesday that Sondland's testimony did not change the White House position that no "quid pro quo" took place.
Taylor and others have testified that it became clear that Trump, through this irregular channel led by Giuliani, was withholding the funds to get Ukraine to investigate conspiracy theories about the 2016 presidential election and the Bidens.
Mr Mulvaney is the highest-ranking White House official to be summoned in the probe, although he is unlikely to comply given the White House's opposition to administration officials cooperating with investigators.
It painted a damning picture of Trump offering a quid pro quo. "I will have Mr Giuliani give you a call", Mr Trump said, according to a rough transcript released by the White House.