The 2004 murder of Klebnikov, editor of the Russian edition of Forbes magazine, drew widespread condemnation and underlined the dangers faced by reporters in Russia.
But his killers — and those who ordered the murder — are still on the loose after two men accused of the killing were acquitted by a jury in 2006.
Investigators this month told Klebnikov family lawyers that they had halted an investigation into the murder, according to a legal document obtained by Reuters.
The Klebnikov family called on Obama to raise the issue when he meets President Dmitry Medvedev and Prime Minister Vladimir Putin next week.
"We want answers, and we are calling on both presidents to make a public statement on this case and the fate of other reporters whose murders in Russia remain unsolved," Klebnikov's brother, Michael, said from New York.
"We are calling on President Obama to show his concern that this case be properly investigated, brought to trial and that justice finally be served," he said. "We are calling on President Medvedev to reaffirm Russia's commitment to solve this murder despite five years of failure to bring this case to a successful conclusion."
The United States has repeatedly pressed Russia to bring Klebnikov's murderers to justice.
But the chief investigator on the case said in a letter to lawyers representing Klebnikov's family that the murder investigation had been halted. "I inform you that on 28 May 2009, the preliminary investigation into case 18/346222-05 on the murder of P. Klebnikov … has been halted," said the letter from the investigator, Petros Garibyan.
A spokesman for the Investigative Committee declined to comment. Garibyan declined to comment.
A Russian legal source, who refused to be identified because of the sensitivity of the case, said the investigation had been resumed after new evidence was uncovered, but a representative of the Klebnikov family said they had received no such notification.
Klebnikov, a U.S. citizen whose grandparents fled Russia during the 1917 Revolution, reported on a world where Russian business, politics and organized crime overlap.
He was shot as he left his office in central Moscow on July 9, 2004.
The trial of two Chechens — Kazbek Dukuzov and Musa Vakhayev — whom prosecutors said had carried out Klebnikov's murder ended with their acquittal. The Supreme Court ordered a retrial, but it was halted in 2007 because Dukuzov could not be tracked down. Prosecutors have released no details about who is suspected of ordering the killing.
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