"The car crashed into the blast wall and the guards of the embassy shot the terrorist but he went and blew himself up," al-Moussawi said.
"The same thing happened with the Iranian embassy."
The authorities said they foiled two other attacks aimed at diplomatic targets by stopping suspected bombers' vehicles and defusing their explosives.
|The explosions in Baghdad on Sunday were the first to shake the capital in recent weeks [AFP]
Hasan Kazemi Qomi, the Iranian ambassador, said it was unclear whether his embassy was a target in the attacks.
"The explosion happened at the embassy gate, targeting visitors and Iraqi police," he told the AP news service. "There was some damage to the embassy building but no employees were harmed inside."
After the explosions, smoke could be seen rising above the city as helicopters circled overhead and gunfire echoed through the streets.
The attacks come a day after uniformed gunmen left 25 people deadin the village of Albusaifi just to the south of the capital.
Some of the victims were members of the Iraqi security forces while others were part of local Awakening Councils or Sahwa, which are comprised of Sunni fighters who allied with US forces to combat al-Qaeda in Iraq.
The blasts also come at a time of political uncertaintyfor Iraq following last month's inconclusive parliamentary elections.
Al Jazeera's Zeina Khodr, reporting from Baghdad, said the attacks appeared to have confirmed fears that security could deteriorate due to the political instability.
"This has been the real fear, the very fact that the security situation could destabilise simply because of the political negotiations taking place to form a new Iraqi government," Khodr said.
The result of the election has triggered a bout of political wrangling as Iyad Allawi, the former prime minister, tries to form a government after winning a narrow victory in the polls. Analysts say the uncertainty could last for weeks.
"The terrorists seized this time between the end of the elections and the forming of the government to target the political process," said Abdul-Rasoul al-Zaidi, an Iraqi civil defence official.
In the hours before Sunday's blasts, Iraq's Green Zone, site of many international agencies and government buildings in the capital, came under mortar fire.
Meanwhile, a car bomb in the restive northern city of Mosul killed three people and wounded 25 others, including seven policemen thought to be the target of the attack.