The authenticity of the statement, posted on a website commonly used to claim responsibility for such attacks, could not be independently confirmed.
"Suicide bombers targeted the dens of infidelity and pillars of the rejectionist Shia state in the land of the caliphate," the statement read.
The attacks were the deadliest seen in Iraq in two years, targeting the justice ministry and the Baghdad provincial administration and raising fears about Iraq's ability to protect itself as it prepares for the US military withdrawal.
"The bloody Sunday explosions strengthen Iraq's demand to the UN and the Security Council to nominate a senior international envoy to come to Iraq and evaluate the degree of interference targeting stability in Iraq," Zebari told al-Arabiya television.
"I believe this will be achieved soon, especially after [Sunday's] explosions confirmed that this issue is vital and important. We need the help of the international community."
"The blood of Iraqis is very cheap and I ask, how many victims will it take to convince the government that it has totally failed?"
Hameed Salam, former Iraqi army officer
A spokeswoman for Ban Ki-moon, the UN secretary-general, said he was awaiting a response from the Security Council.
"The secretary-general himself wants to wait on this until he gets some clear view on what the Security Council wants," Michele Montas told reporters in New York on Monday.
In Washington the state department said the US backed an inquiry to see if there has been any foreign involvement in the attacks.
"We would support the idea of the UN appointing a senior official to go into Iraq and look into these very serious allegations," Ian Kelly, a department spokesman, said.
"What happened was so utterly horrific that the circumstances surrounding it need to be looked into."
Grief and anger
Zebari's call comes amid growing public anger in the wake of the bombings, which occurred close to the heavily-fortified Green Zone.
|Sunday's attacks have provoked widespread international condemnation [AFP]
As grief turned into anger on Monday Iraqis attending funerals of some of those killed accused the government of a major security breach that saw the two suicide truck bombers penetrate what was supposed to be one of the safest areas in the capital.
"The blood of Iraqis is very cheap and I ask, how many victims will it take to convince the government that it has totally failed?" Hameed Salam, a former army officer now driving a taxi, said.
Many criticised Nouri al-Maliki, the Iraqi prime minister, for what they said was his government's failure to improve the security situation.
"Al-Maliki is always on TV bragging that the situation is stable and security restored," Ahmed Mahmoud said at the Yarmouk hospital after finding the remains of his brother.
"Let him come and see this mass destruction," he told The Associated Press news agency.
The co-ordinated bombings were the deadliest since a series of massive lorry bombs in northern Iraq killed nearly 500 villagers from the minority Yazidi sect in August 2007.
In Baghdad itself, it was the worst attack since a series of suicide bombings against Shia neighbourhoods in April 2007 killed 183.
The Iraqi government has blamed Sunday's attacks and the bombings on August 19 that devastated the Foreign and Finance Ministries, on al Qaeda and supporters of Saddam Hussein's outlawed Baath party.
Jawad al-Bolani, the Iraqi interior minister, said 76 people have been arrested so far, but he did not provide further details.
"This is a terrorist act," he said, calling on all the political forces to co-operate and assist the Iraqi security forces.
Bryan Whitman, a Pentagon spokesman, said the US military was providing bomb disposal and forensic help to Iraqi authorities.
Underscoring the continued security problems on Monday four people were killed in a car bomb blast at a police checkpoint near Karbala in southern Iraq.
Seven others were wounded in the incident.
Meanwhile Michael Ratney, a US State Department spokesman, told Al Jazeera that the latest attacks in Baghdad will not affect the scheduled US troop withdrawal.
"We have an agreement that we have announced to pull combat troops out by August of next year and the rest by the end of 2011… that has not changed in any way," Ratney said.
He said there were adequate forces between the Iraqi and US sides to provide for security to ensure that the elections set for January proceed on time and in a peaceful way.