House investigators issued subpoenas on Thursday to compel Mr. Parnas and Mr. Fruman to sit for depositions in the impeachment inquiry, just hours after the men were indicted.
During a 2017 meeting in the Oval Office with Mr. Trump and the secretary of state at the time, Rex W. Tillerson, Mr. Giuliani pushed for help to secure the release of a jailed client, an Iranian-Turkish gold trader, as part of a potential prisoner swap with Turkey.
William P. Barr, the attorney general, met privately on Wednesday evening with one of Mr. Trump’s frequent confidants, Rupert Murdoch, the media mogul whose holdings include Fox News, which has recently become more critical of the president.