Falah Hassan Shanshal, a Sadr party member, said al-Auqaeili had been taken to the military hospital in the government and diplomatic Green Zone in the capital for treatment. He later died of his injuries.
The explosion occurred as al-Auqaeili's car passed an army checkpoint in the Habibiyah area near Baghdad's mainly Shia district of Sadr City.
He became the first Iraqi MP to be killed since the April 12, 2007 suicide bombing of the national parliament, where one politician and seven other people died.
Shanshal, who was riding in a different car in the same convoy, said the group became suspicious when discovering there were no traffic jams in the usually crowded area.
He said the "operation was a pre-planned one'' and that the explosion was remote-controlled.
Shanshal demanded a government investigation into how the roadside bomb had been planted so close to the checkpoint.
"We hold the security forces responsible for this attack. They should be responsible for the security of the city," he said.
Nuri al-Maliki, the Iraqi prime minister, vowed to find the killers, saying he had appointed a panel headed by Jawad Bolani, the interior minister, to investigate the assassination.
"We reaffirm our determination to get at the hotbeds of terrorism and crime and arrest and prosecute the killers and bring them to justice," he said in a statement.
Al-Auqaeili was a senior member of al-Sadr political bloc, which has 30 seats in the 275-member parliament. The attack raised concerns of a rise in violence before provincial elections scheduled to be held in 14 of Iraq's 18 provinces next year.
Major General Michael Oates, US military commander of eight provinces in southern Iraq, on Thursday said that the potential for manipulation of provincial elections from both inside and outside Iraq posed a major security threat.
"Violence as we go into the election cycle is likely to increase," he told a news conference in Baghdad.
|A roadside bomb in Baquba targeted a Sunni leader working with US forces [AFP]
A second roadside bomb exploded on Thursday in Sadr City, killing one Iraqi civilian and wounding four others, including two policemen.
Sadr City and the surrounding areas have been dominated by al-Sadr's al-Mahdi army militia and was the scene of fierce clashes between it and US and Iraqi forces earlier this year.
The area has been relatively peaceful after al-Sadr declared a ceasefire and the Iraqi security forces assumed control in late May.
However, tensions have been rising over the US-Iraqi security talks on a deal that would replace the UN mandate for US forces, which expires at the end of the year.
An Iraqi Sunni army leader working with US forces was killed in a roadside bomb along with two of his children and nephew on Thursday in the city of Baquba, security officials said.
Abbas Khudair, who heads Sahwa, or the Awakening group, which is paid by American forces, was targeted as he drove with his family in the Al-Uthaim area in Baquba.
Meanwhile, Firas al-Juburi, a policeman, said another Sahwa leader was shot dead in the northern oil city of Kirkuk on Wednesday night by unidentified fighters.
Al-Qaeda has been blamed by the US military for most of the brutal violence in Iraq since the fall of Saddam Hussein, Iraq's deposed leader.