"The priority now is security ... it affects all other issues, such as the economy and rebuilding," Jaafari told a news conference to announce his nomination.
He said if he became prime minister he would work to improve the capability of security forces and increase their numbers.
The bearded, 58-year-old still faces a challenge from incumbent interim Prime Minister Iyad Allawi.
But Allawi's list won only 14 percent of the vote in the election, while the Shia alliance won 48 percent - enough for a majority in the National Assembly - and has insisted on having the top job.
Jaafari, a physician and father of five, was a member of the US-appointed Governing Council that ran Iraq after the 2003 war. He joined Dawa - Iraq's oldest Islamic movement - in 1966, but fled to Iran in 1980 after a crackdown on the party in which thousands of his comrades were killed.
Insurgents reminded the future government of the challenges it will face by detonating a car bomb near an Iraqi army convoy as it left Baghdad's fortified Green Zone. Two soldiers were killed and 30 wounded by the blast, which sprayed shrapnel over a wide area and could be heard across the city.
Human rights group Amnesty International also gave Iraq's future leaders food for thought, publishing a report which said Iraqi women were no better off now than under Saddam Hussein.
The report, entitled "Iraq - Decades of Suffering", accused some US soldiers of abusing Iraqi women. Washington said it would study the report and investigate the allegations.
In a Shia area of Baghdad, an Iraqi army brigade became the first in the country to take control of its area from US -led forces - a symbolic moment the Americans hope will be repeated across the country, allowing it eventually to withdraw its 150,000 troops.