A US diplomat told Donald Trump Ukraine would carry out investigations the president had asked for, a US official testified at the impeachment inquiry.
State department official David Holmes said he had overheard this during a call in July between Mr Trump and the US envoy to the EU, Gordon Sondland.
Mr Holmes said the call came a day after Mr Trump asked Kyiv to probe ex-Vice-President Joe Biden.
Mr Trump has dismissed the impeachment inquiry as "presidential harassment".
The inquiry is investigating whether Mr Trump withheld US military aid to Ukraine in order to pressure the country's new President Volodymyr Zelensky to announce a corruption inquiry into Mr Biden, now his rival for the US presidency.
On Friday, Mr Trump launched a Twitter attack on another witness - former US ambassador to Ukraine Marie Yovanovitch.
"Everywhere Marie Yovanovitch went turned bad," Mr Trump wrote in the middle of her testimony. "She started off in Somalia, how did that go?"
Asked for her response, Ms Yovanovitch called it "very intimidating".
Mr Trump later hit back, arguing his tweets were not intimidating "at all". He told reporters he had watched part of the impeachment hearing and considered it "a disgrace".