Two of President Trump’s top envoys to Ukraine worked on a statement for the country’s new president in August that would have committed Ukraine to pursuing investigations sought by Mr. Trump into his political rivals, according to three people briefed on the effort and documents released Thursday night.

Their work on the statement is new evidence of how Mr. Trump’s fixation with conspiracy theories linked to Ukraine began driving senior diplomats to bend American foreign policy to the president’s political agenda in the weeks after a July 25 call between the two leaders.

The statement was worked on by Gordon D. Sondland, the United States ambassador to the European Union, and Kurt D. Volker, then the State Department’s special envoy to Ukraine, according to the documents and the three people who have been briefed on it. Rudolph W. Giuliani, Mr. Trump’s personal lawyer and the de facto leader of a shadow campaign to push the Ukrainians to press ahead with investigations, provided the critical element of the language, Mr. Volker told House Democratic investigators on Thursday, a person familiar with his testimony said.

The Ukrainians never released the statement. But if they had, Mr. Trump’s aides would have effectively pressured a foreign government to give credence to allegations intended to undercut one of the Democratic Party’s leading 2020 presidential candidates — former Vice President Joseph R. Biden Jr. — without leaving Mr. Trump’s fingerprints on it.

Mr. Volker spent Thursday on Capitol Hill being questioned by House investigators as Democrats pursued their impeachment inquiry into Mr. Trump’s actions.

Late Thursday, House Democrats released a series of texts between Mr. Volker and Mr. Sondland including the language for the proposed statement. On the morning of Aug. 13, Mr. Volker sent Mr. Sondland what appears to be language they wanted added to an earlier draft sent by the Ukrainians.

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