“It said ‘Congratulations, you ran a great campaign.’ ‘Oh, thank you, Mr. President, look forward to working with you,’” Mr. Cramer said.

The president’s thinking seemed to be that the congratulatory April call might draw attention away from his July exchange with Mr. Zelensky in which he pressed the Ukrainian president to investigate former Vice President Joseph R. Biden Jr. and a discredited theory about Democrats conspiring with Ukraine to interfere in the 2016 election. Democrats consider a reconstructed transcript of that call their most damning evidence against Mr. Trump.

The House Intelligence Committee plans to convene another impeachment hearing on Friday, calling Marie L. Yovanovitch, the former American ambassador to Ukraine whose ouster by Mr. Trump, some members say, set the stage for his pressure campaign.

The Intelligence Committee convened the House’s first public impeachment hearing in two decades on Wednesday with testimony from William B. Taylor Jr., the top American diplomat in Ukraine, and George P. Kent, a senior State Department official responsible for policy toward the country.

They told the committee that Mr. Trump and his allies inside and outside the government placed the president’s political objectives at the center of American policy toward Ukraine, using as leverage both the security assistance that Congress had appropriated for Ukraine’s war with Russia as well as a White House meeting that was coveted by the country’s new leader.

The new witness who emerged on Thursday, Suriya Jayanti, a State Department official in Kiev, would be able to describe a phone call she overheard between the president and Gordon D. Sondland, the United States ambassador to the European Union, in which they discussed the investigations Mr. Trump sought. Ms. Jayanti sat at a restaurant with Mr. Sondland and at least one other embassy official, David Holmes, as Mr. Sondland and Mr. Trump spoke by phone in July, according to two people briefed on the matter.

During that call, Mr. Trump brought up the investigations he sought and Mr. Sondland said the Ukrainians were prepared to move forward with them. After the call, Mr. Sondland told at least Mr. Holmes that Mr. Trump cared more about the investigations his personal lawyer Rudolph W. Giuliani had been pushing the Ukranians to commit to than about Ukraine.