Last Wednesday, the Moscow City Court suspended hearings in the murder case as one of the defendants, Kazbek Dukuzov, failed to appear in court, and the judge issued a warrant for his arrest.
The statement said that the family asked for an open trial and that all of the defendants in the case should be held in custody.
Another defendant in the case, Musa Vakhayev, had given a pledge not to leave the city and attended the court session last Wednesday.
Both men were released from detention in May 2006 after a Moscow court declared them not guilty of murdering the Forbes editor in Moscow in July 2004.
Vakhayev and Dukuzov failed to appear at a court session February 15, and hearings had to be postponed.
A third suspect, Fail Sadretdinov, was also cleared of murder charges last May, but sentenced in January to nine years in prison for property fraud in a separate case relating to his work as a public notary.
Sadretdinov's lawyer, Ruslan Koblev said last Wednesday that Dukuzov was allegedly in the hospital in Chechnya, and that the defense team had asked hearings to be postponed for a week.
However, the court supported the prosecutors and issued an arrest warrant.
Koblev also said the defense team intended to seek an open trial, and quoted Sadretdinov as saying that "new materials, which could have been fabricated, appeared in the case."
A U.S. journalist of Russian descent, Klebnikov, 41, worked for Forbes since 1989 and became the first editor of Forbes Russia when it was launched in April 2004. He earned himself an international reputation for investigating murky business dealings and corruption in the post-Soviet era.