Two major Sunni organisations - the Association of Muslim Scholars (AMS) and the government's Sunni Endowment - said bodies of 11 Sunni men were found on Wednesday hours after they were taken by Iraqi security forces in early morning raids.
The dead included Sunni cleric Dia Muhammad al-Janabi, a member of the AMS. A colleague, Shaikh Hassan Sabri Salman, said al-Janabi had been taken to a house in a Shia neighbourhood "where they were tortured before being executed".
Adnan al-Dulaimi, head of the state-run Sunni Endowment, which takes care of Sunni mosques in Iraq, stopped short of blaming state security forces but said the Sunnis were taken away by armed men "in military uniform".
"The government and the American forces that are responsible for the security of the Iraqi people should investigate this matter," he told Aljazeera.
Mainstream Sunni parties and organisations were already in an uproar over the deaths of at least nine Sunni men who died this week in police custody. The men were rounded up following a gun battle on Sunday in west Baghdad.
Police delivered their bodies to Yarmouk hospital the following day. The Interior Ministry says it has launched an investigation into their deaths. Major-General Hussein Kamel said it appeared the Sunnis suffocated after they were locked in a police van whose air conditioning failed in the 43C heat.
"The government and the American forces that are responsible for the security of the Iraqi people should investigate this matter"
Kamel said that if the investigation found evidence of criminal conduct on the part of the police, the case would be referred to the courts. The country's largest mainstream Sunni political group, the Iraqi Islamic Party, denounced "this savage crime" which shows the "barbaric way citizens are being treated".
Presidential adviser Wafiq al-Samarie, a Sunni and a former intelligence chief under Saddam Hussein, acknowledged that Iraq's new security forces lacked training and experience.
Al-Samarie said Sunni clerics had a duty to speak out against alleged atrocities committed against their community "but they should denounce strongly and clearly the terror" committed by anti-US fighters "so as not to accuse one side of all the crimes".
Sunni allegations follow a statement this month by Britain's Defence Ministry and Foreign Office that they were "deeply concerned" by reports of the abuse of terrorist suspects in Iraqi police custody.
Neither ministry would detail the allegations, but The Observer newspaper of London said this month it had photographic evidence of torture of terrorist suspects by Iraqi security units.
The newspaper did not publish those photographs, but said the allegations included burning, strangulation, sexual abuse, hanging by the arms, the breaking of limbs and, in one case, the use of an electric drill on knee caps.
Some forces, comprising mainly
Shia, are said to abuse Sunnis
Many of the allegations have centred on elite Iraqi units largely made up of Shia Muslims. That threatens to worsen sectarian tensions at a time when Washington is encouraging the Shia-dominated government to reach out to the Sunnis, say analysts.
Al-Dulaimi, who spoke out against the mysterious deaths of the nine Sunnis, has been at the forefront of efforts by moderate Sunnis to convince members of the community to take part in the political process despite threats by fighters.
So far those efforts have brought only limited success - which is now threatened by reports of abuse.
This month, the government took 15 Sunnis onboard a parliamentary committee drafting a new constitution, which is scheduled to be finished by 15 August.
Two of the Sunnis have already quit after receiving threats.