Mr. Rubio did not specify what action was needed to lift the hold.
Last week, Guatemala’s highest court threw out the family’s convictions and sent their case back to the trial judge, with orders to reconsider their case. They could be released from jail this week.
The United Nations commission “has been doing terrific work on a whole host of issues with the attorney general of Guatemala,” said Eric Olson, a Guatemala expert with the Wilson Center in Washington. “It would be unfortunate if this led to some irreparable harm to those efforts.”
Senator Patrick J. Leahy, a Vermont Democrat who has supported the commission, warned against using the Bitkov case to attack it. “If Mr. Velasquez is removed for specious reasons or Cicig is shut down, it would set back the cause of justice and seriously jeopardize U.S. assistance to the government of Guatemala,” he said on Sunday.
The family’s plight caught the attention of William F. Browder, a prominent investor who has led an international campaign to punish Russian human rights abusers. After a Guatemalan court sentenced Igor Bitkov to 19 years in jail, and his wife, Irina, and daughter, Anastasia, to 14 years for using false documents, Mr. Browder began working to free the family. He made Mr. Velásquez and the commission one of his targets.
Mr. Browder argues that the Russian government, through the state-owned bank VTB, pushed for the commission and the Guatemalan attorney general’s office to wrap the Bitkovs into a longstanding investigation into a scheme at the government’s passport office to sell fake passports.
“All of these people who are screaming about the sacred cow of the Cicig are doing an injustice to the Cicig because the Cicig is clearly involved with the Russians in a vendetta against the Bitkov family,” Mr. Browder said in a telephone interview on Sunday.
Cicig said it had identified the Bitkovs’ purchase of the passports independently.
Despite widespread support for the commission in Congress and among members of the Trump administration, Mr. Browder’s zeal for the Bitkovs’ case struck a chord with Mr. Rubio.
Three Republican lawmakers — Senators Roger F. Wicker of Mississippi and Mike Lee of Utah, and Representative Christopher H. Smith of New Jersey — joined Mr. Rubio in writing to the chairmen of the House and Senate committees on foreign relations to suspend funding to the commission.