The harassment escalated a year ago when Iranian authorities began a criminal investigation alleging their work was "a crime against Iran's national security", according to the BBC.
"We urge the Iranian authorities to cease all legal action against BBC Persian staff and their families, and to cease the use of repressive legislation against independent journalism, whether affiliated to BBC or not", the Special Rapporteurs said.
THE BBC has launched an "unprecedented" appeal to the United Nations to protect its Persian service staff, the corporation says journalists at the BBC Persian service have been subjected to a campaign of harassment including death threats.
"In fact, during the past nine years, the collective punishment of BBC Persian Service journalists and their families has worsened", added Hall.
In 2015, the Iranian Culture Ministry said it would let some BBC journalists temporarily work in the country, limiting the maximum duration of stay to one week. "Targeting family members in Iran in an attempt to silence journalists working in London must be stopped; the worldwide community must act now".
BBC Persian "has always focused on striking Iran", he said, citing the 1953 coup d'état of Iran's democratically elected government.
The BBC says its Persian satellite television service journalists in London and their families in Iran have been "systematically targeted" since it launched in 2009.More news: LLC Cuts Holdings in Abbott Laboratories (NYSE:ABT)
"We are concerned at recent reports that the action has now escalated to direct targeting of family members of BBC Persian staff". Since then, Tehran has repeatedly accused the broadcaster of violating Iran's security.
Persian (BBC Farsi) has been banned from Iran since 2010 on the basis of allegations that it was acting against the country's national interest.
These events were documented in the report by the former United Nations special rapporteur on the situation of human rights in the Islamic Republic of Iran, Asma Jahangir (now deceased), which was published in March 2018.
Lawyers for the BBC World Service in October filed an urgent appeal to UN Special Rapporteurs David Kaye and Asma Jahangir on behalf of its Persian Service staff.
BBC staff will address the UN Human Right Council on Monday 12 March.
Iran has often come under intense worldwide criticism for its human rights violations.