The journalists have endured death threats, criminal investigations, the freezing of assets and defamation.
Some relatives have been held in degrading conditions and ordered to tell family members to leave the BBC.
The harassment reportedly intensified when the journalists covered the mass anti-government protests in November.
The unrest prompted a bloody crackdown by the security forces. Amnesty International said more than 300 people were shot dead, while a Reuters news agency report put the death toll at 1,500.
Iranian authorities dismissed those figures, but acknowledged killing some “rioters”.
The strongly-worded statement issued on Wednesday by UN special rapporteurs Agnes Callamard, Javaid Rehman, David Kaye and Michel Forst highlighted the case of a BBC Persian TV presenter who has been the subject of death threats, allegedly by Iranian authorities.
Rana Rahimpour told the UN Human Rights Council on 9 March that she had received a written message saying that she, her children, her husband and her elderly parents would be assassinated within a month.
The message also said that Ms Rahimpour would be the first employee of the BBC to be killed, and that, after her assassination, it would be the turn of other BBC Persian employees.
“These allegations are extremely concerning and if confirmed, would indicate that the Iranian authorities are prepared to use force extra-territorially, in violation of international law,” the special rapporteurs said.
“Harassment, surveillance, death threats against journalists, within and outside domestic boundaries violate international human rights law, including the right to physical integrity, the right to life and the right to freedom of expression.”
They added: “When these acts are conducted extra-territorially, as with BBC Persian Services, these acts violate international law regulating the use of force in times of peace. These ultimately constitute serious threats to global security and thus demand strong reactions on the part of the governments of the countries where BBC Persian Service journalists reside.”
The special rapporteurs said the reactions included “implementing safeguards to protect the integrity of journalists, their families and their profession”.
In a separate development, BBC Director General Tony Hall issued an appeal to the new secretary of Iran’s High Council for Human Rights, Ali Bagheri Kani, saying he hoped it could “open a new chapter in relations between the Iranian authorities and the BBC”.
“Two years ago we offered to talk directly with the Iranian government in a constructive way to find a new way forward. Mr Bagheri Kani could go some way to address the concerns of the international community if he is willing to accept this offer in a positive spirit, without conditions. I very much hope he does,” he said.
Seamus Dooley, assistant general secretary of the National Union of Journalists, said: “The personal testimony of BBC Persian journalists is shocking to hear.”
“It is particularly shameful for the Iranian authorities to target journalists’ children and elderly relatives,” he added.
Source » bbc