WASHINGTON—The White House said it won’t cooperate with the House impeachment probe and the administration blocked the deposition of a U.S. ambassador seen as central to the Ukraine controversy, marking clear battle lines in the fight between President Trump and Democratic lawmakers.

House committees responded by subpoenaing Gordon Sondland, the U.S. ambassador to the European Union, after the State Department early on Tuesday directed him not to appear for his planned testimony.

Later on Tuesday, White House counsel Pat Cipollonesent a letter to congressional Democrats saying the administration would refuse to cooperate with the probe of President Trump’s effort to have Ukraine investigate former Vice President Joe Biden, who is seeking the Democratic presidential nomination. Mr. Cipollone said the impeachment inquiry was an effort to overturn the results of the 2016 election.

“You have designed and implemented your inquiry in a manner that violates fundamental fairness and constitutionally mandated due process,” Mr. Cipollone wrote. “President Trump cannot permit his administration to participate in this partisan inquiry under these circumstances.”

A senior administration official said it was ordering a “full halt” on cooperating with the impeachment probe, which was launched two weeks ago, while not ruling out potential future cooperation.