Mr. Giuliani and Mr. Parnas pressured Ukrainian officials to commit to investigating the arrangement, and some Senate Republicans are threatening to call Hunter Biden to testify in the Senate impeachment trial if Democrats press for their own witnesses.
A spokesman for Mr. Nunes did not respond to a request for comment.
Friday’s release also included correspondence of an obscure Republican candidate for Congress in Connecticut who had suggested to Mr. Parnas that Marie L. Yovanovitch had been under surveillance while serving as the United States ambassador in Kyiv at a time when she had come under heavy criticism from Mr. Trump’s allies.
The newly released correspondence included WhatsApp messages between the congressional candidate, Robert F. Hyde, and an unidentified account with an avatar of a man and a number that began with Belgium’s country code, but was partly redacted in the release. Someone using the account sent Mr. Hyde an official government portrait of Ms. Yovanovitch, and indicated, “My contacts are checking,” adding, “I will give you the address next week.”
Mr. Hyde responded, “Awesome.”
The person using the account appeared to be familiar with Mr. Hyde, congratulating him “on your new business development” while sending updates suggesting knowledge of Ms. Yovanovitch’s whereabouts in Kyiv, Ukraine’s capital.
Mr. Hyde appears to have forwarded some of the contents of the messages to Mr. Parnas, and when the messages between the two men were released this week, they prompted concern from Ms. Yovanovitch, who was removed from her post last spring on Mr. Trump’s orders, and from others.
On Thursday, Ukrainian police announced a criminal investigation into possible illegal surveillance, and F.B.I. agents visited Mr. Hyde’s home and business, according to a law enforcement official.
Mr. Hyde, who has a history of erratic behavior, initially claimed that the messages were a prank, saying on Twitter on Tuesday that he was “playing with” Mr. Parnas.