The call by the Sunni-based Islamic Party follows revelations that some 170 detainees, mostly Sunni, were illegally held at a center run by the Shia-dominated interior ministry, in a case likely to embarrass the US military supervising local security forces.
"We insist on having an international investigation," Islamic Party spokesman Alaa Makki said.
"There have been similar cases in the past and investigations into them led to nothing," said another party spokesman, Ayad Samarrai.
"We want an international and impartial inquiry as we are beginning to think there are people high up in government who are responsible, or at least accomplices."
Makki also blamed US-led forces for the abuse, saying that it could not happen without "their green light".
Iraq Prime Minister Ibrahim Jaafari on Tuesday ordered an investigation into the allegations with a committee due to report its findings within two weeks.
Jaafari's spokesman Laith Kubba told the BBC that the prime minister was "outraged" by the alleged abuse, adding: "It goes pretty much against all the core values that this government holds."
The case came to light after US forces raided the underground facilities of an interior ministry complex in south Baghdad on Sunday.
Hussein Kamal, Iraq's deputy interior minister, told CNN television that he saw evidence of torture. "I saw signs of physical abuse by brutal beating. One or two detainees were paralyzed. And some had their skin peeled off various parts of their body."
The Committee of Muslim Scholars, the main Sunni religious organization in Iraq, accused "interior ministry services of resorting to torture and ransoming prisoners".
Committee spokesman Sheikh Abdel Salam Al Kubaissi said that his organization had "filmed testimony of released detainees who had been tortured" and that the videos were handed over to Arab League chief Amr Moussa when he visited Baghdad last month.
The sheikh also accused "interior ministry services of detaining people at night in their homes on terrorist charges and then torturing them into making confessions, parts of which are then broadcast on television".
Some detainees were released a month or two later "after paying a bribe, with no charges being brought against them", Kubaissi added.
The US embassy and US military issued a statement welcoming the Iraqi government's decision to investigate the case and stressing that the mistreatment of detainees was "totally unacceptable".
US Ambassador Zalmay Khalilzad and General George Casey "have discussed this case with the leaders of the Iraqi government at the highest levels", it added.
A scandal over the abuse by US forces of Iraqi detainees at Baghdad's Abu Ghraib prison last year led to international condemnation of the United States as it struggled to defend the March 2003 invasion and occupation of Iraq.
The United States will provide "technical assistance, including support from US law enforcement elements of the department of justice and the Federal Bureau of Investigation" to help the Iraqi government look into the matter, the US statement added.
The revelations came just a month ahead of general elections to elect a permanent government, the final stage in Iraq's transition to democracy following the ouster of Saddam Hussein.
In London British Foreign Secretary Jack Straw spoke of his "deep shock" and said: "Whoever carried out this abuse must be caught and brought to justice, regardless of rank or background."
The UN mission in Iraq on Monday accused the interior ministry of holding hundreds of individuals in detention despite judicial orders for their release.
Sunni Arabs, who provide the backbone to the insurgency, have repeatedly accused Iraq's security agencies, some of which have allegedly been infiltrated by Shia militias, of engaging in torture and extra-judicial executions.
Meanwhile, the US military announced the loss of three US soldiers following a roadside bomb explosion on Tuesday in Baghdad.
There have been at least 2,072 US military deaths in Iraq since the March 2003 invasion, according to an AFP tally based on the independent Iraq Coalition Casualty Count.
Dissatisfied with the slow pace of progress in Iraq and worried about the growing body count, the US Senate on Tuesday sought to make the White House answerable for its troubled Iraq policy, and pressed President George W. Bush to lay out a clear exit strategy.
However, US Defense Secretary Donald Rumsfeld warned against a precipitous withdrawal of US forces.
Washington wanted to hand over security responsibilities to Iraqis and leave as soon as possible, "but not in a manner that is precipitous, not in a manner that would inject instability into the situation and not in a manner that would suggest to a terrorist that all he has to do is wait us out", he said.
© 2005 Agence France-Presse
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