Barham Saleh, the planning minister, who made a surprise visit to Najaf to meet Grand Ayat Allah Ali al-Sistani, said on Sunday: "I was delegated by President [Jalal] Talabani to explain in detail to Ayat Allah al-Sistani the reasons for our opposition to the nomination of al-Jaafari to the post of prime minister."
He said al-Sistani heard "our arguments and underlined the need for continuing dialogues with other Iraqi factions".
"He also underlined the need to maintain the unity of the Shia United Iraqi Alliance which we also wish," Saleh said.
"We reject al-Jaafari because we believe that Iraq needs a government of national unity and new faces."
The planning minister said he hoped the Shia alliance "will consider our opposition and change the candidate".
"We reject al-Jaafari because we believe that Iraq needs a government of national unity and new faces"
Iraqi planning minister
Saleh also met Shia cleric Muqtada al-Sadr.
"Sadr insisted on national unity and on consolidating the bonds between the Iraqis," said Saleh, adding that al-Sadr had vowed his support for al-Jaafari.
Last month, al-Jaafari was re-selected to lead the next Iraqi cabinet by the Shia alliance.
But he was selected by just one vote, clearly showing a division within the alliance as many voted for Adel Abd al-Mahdi, the vice-president, to replace him.
The Kurds, Sunnis and the secular political factions of Iraq have opposed the candidacy of al-Jaafari to lead the next government, saying he had failed to curb the raging violence during his term.
The prime minister faces strong opposition from the Kurdish group which has 53 seats in the new 275-seat parliament, as well as the Sunni group - the National Concord Front - which has 44 seats and the list of former prime minister Iyad Allawi, who controls 25 seats.
Al-Jaafari's Shia alliance is the largest block with 128 seats.