The decision paves the way for a possible breakthrough in the deadlock on forming a national unity government.
Four months after the elections, leaders have failed to agree on the composition of the first post-Saddam Hussein government.
Work on forming a coalition led by Mr Jaafari's United Iraq Alliance (UIA) has been held up by other parties who accuse him of sectarian attitude.
Political leaders have also bickered over ministerial posts and the formation of cabinet.
UIA to decide
In a televised address, Mr Jaafari said that he would accept whatever the Shia bloc decided.
"I understand the alliance is facing challenges and I feel that my name should not be associated with issues that delay the nation's progress," he said.
"I do not want to be a hurdle in the democratic process," he said, without specifying whether he was withdrawing his candidacy as the next premier.
“I have left the choice with them [the UIA], to do whatever they want,” said Mr Jaafari.
Rescheduled meeting
The UIA is expected to meet over the weekend, ahead a parliamentary session which was postponed on Thursday.
The session was cancelled at the request of the UIA, which is now planning to vote on a new candidate for the post of premier before the Saturday session.
It will be the second session since the general election in December.
US presssure
The US and its allies want a new representative cabinet to avert the threat of civil war.
Washington regards it as the final phase in Iraq's political transition since the US-led invasion of March 2003.
It is hoped that it would pave the way for an eventual withdrawal of its troops.
The inaugural session of parliament was held on March 16 but was swiftly adjourned amid few signs of a deal on the government.
News of the cancellation of Thursday's session came shortly after Mr Jaafari announced his backdown.
"The leaders decided that the session be postponed until Saturday 3pm so we can give more time for consultations and negotiations in order to overcome all the obstacles," acting parliament speaker Adnan Pachachi told reporters.
"I believe if we give ourselves this time, we will be able to succeed in forming a national unity government which people have been waiting for."
"The alliance's political body will decide on a candidate and call for voting on him before Saturday's parliament session," said Hussein al-Shahristani, a UIA lawmaker.
He said the alliance requested the session's cancellation to make time for the finalisation of candidates for the key parliamentary posts.
"We want to have a national unity government and to do that we need to agree on all the nine parliamentary posts," Mr Shahristani said.
"When we meet on Saturday we must have all the names for the nine posts."
Blocs debate candidates
Iraq's various parliamentary blocs are currently debating on candidates for the posts of the three-member presidential council, two deputy premiers, one parliament speaker and his two deputies, apart from the prime minister.
It was not immediately clear if the UIA had decided to drop Mr Jaafari in favor of another candidate.
Shiite MP Jawad al-Maliki earlier in the day indicated that Jaafari might step down.
"Jaafari has left the decision about his candidacy with the alliance. That means he is no longer insisting on the post," he said.
Mr Jaafari's role has been the main sticking point in forming a broad coalition.
Sunni Arab and Kurdish politicians oppose him, complaining that he
has failed to curb the rampant violence in Iraq or achieve consensus.
The doctor-turned-politician was selected as the Shiite premier candidate by a single vote in February, beating Vice President Adel Abdel Mahdi.
The UIA holds 128 seats in the 275-member parliament.
That means that without the support of the Sunnis and Kurds it is unable to form a power-sharing government as envisaged by the United States.
On Thursday, lawmaker Mahmoud Othman said Jalal Talabani was being considered to stay on as president, Mahdi to remain as one vice president, and Sunni Tareq al-Hashemi as the other vice president.
Meanwhile, bloodshed on Thursday left at least 12 people dead in rebel shootings and bombings, while a group of armed men dressed in police uniforms kidnapped six people from two Baghdad bookstores, the interior ministry said.