Six leading human rights organisations have called on Iran to the end the "arbitrary" house arrest of opposition leaders Mir Hossein Mousavi and Mehdi Karroubi, who have been cut off from the outside world for nearly two years without being put on trial.

"For two years now Iranian officials have stripped these opposition figures of their most basic rights without any legal justification or any effective means of remedy," the Iranian Nobel peace prize laureate, Shirin Ebadi, said in a joint appeal signed by Amnesty International, Human Rights Watch, International Campaign for Human Rights in Iran, International Federation for Human Rights, League for the Defence of Human Rights in Iran, and Reporters Without Borders.

"They and their families should not have to endure even one more day under these wholly unjustifiable and abusive conditions," she said.

In mid-February 2011, following calls for street protests in solidarity with the pro-democracy movements in Egypt and Tunisia, dubbed the Arab spring, Iranian authorities placed Mousavi and Karroubi, along with their wives, Zahra Rahnavard and Fatemeh Karroubi, under house arrest.

Security forces initially blocked access to the houses of each couple in Tehran and did not allow them to leave, or their family members to enter the premises. Within a few weeks, the authorities who had surrounded the area entered the residences, ransacking rooms and confiscating documents, limiting the movements of the opposition leaders in an unprecedented fashion. Since then the authorities have released Fatemeh Karroubi from house arrest but increased the restrictions on the remaining three.

The Islamic republic has so far refused to put the men on trial and the decision behind the house arrests is believed to have come from the very top, Iran's supreme leader, Ayatollah Ali Khamenei.

Mehdi Karroubi during the 2009 election campaign. Photograph: Raheb Homavandi/Reuters

Mohammad Taghi Karroubi, one of Karorubi's sons who is currently living in exile in London, told the Guardian that for the last 18 months his father had been made to live in an apartment alone, at one point being denied family visits. "It's solitary confinement. These days he's allowed to visit family members once a week but there was a time we had no contact with him for over four months."

According to the son, Karroubi has access to a small number of books, such the Qur'an and a few poetry books, and is only allowed to watch state television. "He is an old man, hence they gave him ingredients and he has to cook for himself. They don't let my mum stay with him because by separating the two, they are in fact increasing pressure on him."

Despite the pressure, Karroubi had no regrets and was even more determined, the son said.

Mousavi and Karroubi, both presidential candidates in Iran's 2009 elections, alleged the vote was rigged in favour of Mahmoud Ahmadinejad, who took the office for a second term. Millions of protesters who took to the streets chanting "Where is my vote?" were confronted by riot police with batons, teargas and shootings. Tens of protesters were killed and hundreds of activists and journalists were arrested; many are still in jail.

Earlier this week security officials in Iran picked up two daughters of Mousavi, Zahra and Narges, and one of Karroubi's sons, Hossein, from their houses in Tehran and questioned them for several hours before releasing them. They were apparently under pressure for speaking out about the plight of their parents.

On Thursday the foreign office minister for the Middle East and North Africa, Alistair Burt, said Iran's mistreatment of the opposition leaders and their family members demonstrated "a cynical attempt" to suppress them in defiance of the country's obligations under international law.

"This week marks two years of the continued house arrest of Iranian opposition leaders Mir Hossein Mousavi and Mehdi Karroubi," Burt said. "Once again I call on Iran to release Mousavi and Karroubi and to respect the rights of all Iranian citizens to freedom of movement and expression."

Iran is due to hold its next presidential vote in June. Five months out, the authorities have escalated the crackdown on the press, arresting a number of journalists and forbidding any mention of an election boycott. Under Iranian law Ahmadinejad cannot run for a third term.

"The upcoming presidential election in June in Iran cannot have any semblance of legitimacy as long as two candidates from the 2009 election are held under house arrest," said Hadi Ghaemi, the executive director of International Campaign for Human Rights in Iran (ICHRI).

"There is no justification that these illegal detentions have continued for nearly two years now, without any charges to speak of, no rule of law, absolutely no judicial process. The Supreme Leader is ultimately responsible and must immediately release these opposition leaders," Ghaemi said.

According to the ICHRI, the United Nations Working Group on Arbitrary Detention said last year that the house arrests were "arbitrary and thus prohibited" and called on Iran to immediately release the detainees and compensate them for their wrongful imprisonment.