In a case that sparked international outrage, Beheshti who wrote a blog critical of the government, was arrested on October 30 and died some days later after saying he had received death threats and was being tortured in jail.
"It is imperative that people who are potentially involved in committing such gruesome crimes are investigated and brought to justice, as failure to do so promotes a culture of impunity," said Ahmed Shaheed, special U.N. rapporteur on human rights in Iran.
Shaheed and other U.N. experts welcomed Iran's decision to investigate the 35-year-old's death and said the findings should be made public.
"On 6 November, prison authorities contacted family members of Mr. Beheshti to collect his body. Although the circumstances around his death remain unclear, allegations suggest he might have been tortured to death during his investigation," they said in a joint statement issued in Geneva.
Christof Heyns, special rapporteur on extrajudicial, summary or arbitrary executions said whenever someone dies as a result of injuries sustained while in custody, "there is a presumption of state responsibility."
The experts, who report to the U.N. Human Rights Council said there had been several cases reported of detainees dying in custody due to mistreatment or torture, lack of medical attention or neglect.
They called on Iran to release journalists and bloggers jailed in violation of a U.N. treaty on civil and political rights.
Iranian authorities have arrested seven people suspected of involvement in Beheshti's death, a lawmaker said on Wednesday. The suspects' identities have not been disclosed.
The Beheshti case has renewed international concerns about human rights in Iran. In October, the European Parliament awarded its human rights prize to Nasrin Sotoudeh, a lawyer who, opposition websites report, is on hunger strike in prison.
(Reporting by Stephanie Nebehay; Editing by Robin Pomeroy)