Iran has been accused of torturing to death a blogger who was arrested last week for criticising the Islamic republic on Facebook.

Iran's cyber-police, known as Fata, picked up Sattar Beheshti from his home in Robat-Karim last week on suspicion of "acting against the national security" because of his online activities on social networking sites. He was then taken to Tehran's notorious Evin prison.

Beheshti's family heard no news of him until Wednesday, when they were phoned by prison officials asking them to collect his body from the Kahrizak coroner's office. The opposition has accused Iranian officials of torturing the 35-year-old blogger to death.

Beheshti's body was washed according to Islamic rituals on Thursday in Behesht-e-Zahra's cemetery, south of Tehran, and later buried in his home town amid a tight security presence. Only one family member was allowed to attend the ceremony, carried out by security officials.

Kaleme, a news website close to the opposition leader Mir Hossein Mousavi, was the first to report the blogger's death. Iran's state media have largely refrained from reporting on Beheshti's case but the site Baztab, affiliated to Mohsen Rezaei, a former senior commander of the Revolutionary Guard, confirmed his death.

"Sattar Beheshti, who was arrested by Fata [cyber] police, has died while being interrogated," Baztab reported.

Before his arrest, Beheshti had complained on his blog of being threatened by the authorities. "They threatened me yesterday that my mother would wear black because I don't shut my mouth," he wrote. Beheshti had been arrested previously for his activism.

"I told them [the officials] that I only write what I see and what I hear but they responded that they would do everything they can to shut me up, to stop me from spreading news. They said they will shut me up in a way that no name or sign would remain of me," he wrote.

While in jail, Beheshti had officially complained that he was mistreated and tortured, according to Kaleme, which published a copy of his letter on its website.

Iranian authorities have so far refused to comment on Beheshti's death or the allegations of torture but one MP, Mansour Haghighatpour, who sits on the parliamentary committee on national security, told the semi-official Ilna news agency it was not necessary for parliamentarians to investigate the situation.

Beheshti's death, which shocked the country's online community, has highlighted the treatment of political prisoners in Iran. Mohammad-Javad Larijani, the head of the Iranian judiciary's human rights council claimed earlier this year that there were no political prisoners in the Islamic republic.

Human rights activists have long accused Iran's rulers of gross human rights violations, including depriving political prisoners of their right to access proper legal representation. In the light of the accusations, the United Nations has appointed a special rapporteur, Ahmed Shaheed, to investigate alleged abuses in the country.

In October, Shaheed published a detailed report criticising Tehran for the harassment of its imprisoned activists, who he said were subjected to mock executions, rape, sleep deprivation and threats to their families.

Shaheed told the Guardian he was disturbed by the news of Beheshti's death and would investigate it promptly.

Speaking from Tehran, an Iranian blogger said: "It could have been me. Sattar was an ordinary blogger like me, like thousands of other bloggers in this country."

The blogger added: "Just imagine how terrible this is for Sattar's mother … they arrested her son last week and gave her his dead body today and didn't even allow her to attend her son's funeral … I'm just speechless."

Beheshti is not the first person to die in an Iranian jail. After the disputed presidential election in 2009 several activists and protesters died in jail, including at least three confirmed to have died in Kahrizak detention centre.

Many protesters are believed to have been tortured to death in Kahrizak, and several claim to have been raped. An Iranian doctor who examined the victims of Kahrizak was shot dead in September 2010.

Kahrizak became a scandal for the regime when Mohsen Rouholamini, the son of a former senior adviser to the Revolutionary Guards, was named among prisoners who had died at the centre.

Evin prison is home to some of Iran's most respected activists and politicians. Among them are the prominent human rights lawyer Nasrin Sotoudeh, who is currently on a hunger strike with fellow inmates in protest at their mistreatment behind bars.