The testimony from Taylor, the top US diplomat in Ukraine, further connects the Trump administration to a quid-pro-quo agreement involving Ukraine that is now at the heart of the House impeachment inquiry.
In his new statement, Sondland said that by the beginning of September "in the absence of any credible explanation", he concluded that the withheld aid was linked to Trump's demand that Ukraine publicly acknowledge an investigation.
Separately on Tuesday, House investigators released text messages from Taylor in which he expressed concerns to Volker that he was "struggling" with a decision to take the top Ukraine job because he was anxious whether anyone could "succeed with the Giuliani-Biden issue swirling for the next 18 months".
"Ambassador Taylor makes clear why this military aid and continued bipartisan support for Ukraine are so critically important - and why these efforts to undermine US foreign policy for domestic political reasons were so damaging", the statement said.
The Democrats are investigating Trump's requests for Ukrainian action as the USA withheld military aid from the country, which faces threats from its neighbor Russian Federation.
Kent, who heads the European and Eurasian bureau at the State Department, expressed concerns about White House efforts to remove the then-ambassador to Ukraine, Marie Yovanovitch.
Taylor's October testimony appeared to rock some Democratic members of the committees who questioned him.
Democrats have claimed it is evidence of quid pro quo. That is true. In this case, here you had an instance where everyone that I spoke with in the policy side of the administration - you know, Pentagon, military, civilian, State Department, National Security Council - they all thought this is really important to provide this assistance, ' he said.
Yovanovitch herself told investigators she was ousted because Trump's personal lawyer Rudy Giuliani and others wanted her out of the way as they conducted Ukraine policy outside traditional diplomatic channels.
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Taylor said he understood the reason for investigating Burisma was to cast Biden, the former USA vice president, "in a bad light", according to the latest transcript.
Schiff said the closed-door testimonies have offered an "increasing appreciation for just what took place during the course of the a year ago and the degree to which the president enlisted whole departments of government in the elicit aim of trying to get Ukraine to dig up dirt on a political opponent". "But if I understand this correctly, you're telling us that Tim Morrison told you that Ambassador Sondland told him that the president told Ambassador Sondland that Zelensky would have to open an investigation into Biden?"
Democratic lawmakers are pressing for a formal impeachment based on allegations that President Trump during his July 25 call with Ukrainian President Volodymyr Zelenskiy had withheld military aid to pressure Ukraine into investigating former Vice President Joe Biden and his son Hunter.
On Wednesday, Sen. Lindsey Graham (R-S.C.), the chairman of the Senate Judiciary Committee, offered a new defense, suggesting that the Trump White House was too inept to execute a quid pro quo.
His three-page update, tucked beneath hundreds of pages of sworn evidence from Mr Sondland and former Ukraine special envoy Kurt Volker, was released by House investigators as Democrats prepared to push the closed-door sessions to public hearings as soon as next week.
All three have already testified behind closed doors in the first phase of the investigation.
Volker, in his own text messages that he provided to investigators, shares conversations seeking to get a White House meeting between Zelensky and Trump.
As the president referenced, Volker also rejected the notion of a quid pro quo.