WASHINGTON—A top U.S. diplomat told House committees last week that efforts by President Trump and his allies to press Kyiv to open investigations in exchange for a White House meeting with Ukraine’s president amounted to a quid pro quo, his lawyer said.

Gordon Sondland, the U.S. ambassador to the European Union, told House committees that he believed Ukraine agreeing to open investigations into Burisma Group—a gas company where Democrat Joe Biden’s son once served on the board—and into alleged 2016 election interference was...