The heads of the committee said they will consider issuing criminal referrals to subpoenaed individuals who refuse to cooperate.
"While Mr. Meadows and Mr. Patel are, so far, engaging with the Select Committee, Mr. [Steven] Bannon has indicated that he will try to hide behind vague references to privileges of the former President," the statement said. "The Select Committee fully expects all of these witnesses to comply with our demands for both documents and deposition testimony."
On Thursday, US media reported that Trump's lawyer asked his former officials under subpoena to not provide testimony or documents in the investigation and to invoke executive privilege.
Meadows, Patel, Bannon, and former White House Deputy Chief of Staff for Communications Daniel Scavino were required to provide all requested documents to the committee by Thursday and are expected to testify before the panel on October 14 and 15.
On January 6, Trump supporters stormed the Capitol in Washington, in an effort to prevent certification of Joe Biden's victory in the 2020 presidential election. As a result of the riot, a protester and a policeman were killed, and three more died from causes unrelated to the violence.