"We expect that you will call each of the witnesses listed above to ensure that the Democrats" "impeachment inquiry' treats the President with fairness, as promised by Speaker Pelosi", wrote Rep. Devin Nunes of California, the ranking Republican on the Intelligence Committee. "It's a witch hunt and it should never happen to another president".
Thornberry, the top Republican on the House Armed Services Committee, added: "I believe it was inappropriate".
House Republicans over the weekend submitted a list of witnesses they would like to call for public testimony during the impeachment inquiry, but Schiff - who is running the probe - was swift to reject the request to have the whistleblower come forward.
According to the report, the first witness House Republicans want to hear from is Hunter Biden, the son of former Vice President Joe Biden, and the whistleblower who filed the initial complaint that led to the impeachment inquiry against President Trump.
Trump has dismissed all allegations of misconduct.
Democrats, who control the House of Representatives, must approve witness requests submitted by Republicans.
Biden's work for Burisma is an issue in the impeachment inquiry into whether Trump abused his power by asking that Ukrainian leaders to investigate the Bidens at the same time that he was withholding military aid from their country.
But he vowed the inquiry would not be "a vehicle to undertake the same sham investigations into the Bidens... that the president pressed Ukraine to conduct for his personal political benefit".
The White House released a memo of the July 25 call at the center of the inquiry, which Graham referred to in his interview, that shows Trump asking Ukrainian President Volodymyr Zelensky for "a favor" and later asking him to "look into" Biden.
Gordon Sondland, the US ambassador to the European Union, revised his testimony last week to admit he had linked unfreezing almost $400 million in military aid to Ukraine in exchange for Kiev publicly opening the investigations.
The impeachment hearings have been held behind closed doors but will be held in public starting next week. Around three quarters of the United States population watched at least some of the Watergate hearings on television.