Al-Ja'fari and other politicians are jockeying for the top positions in the next government after last month's parliamentary elections.
Al-Ja'fari called for bringing the Sunni minority into the political process. Sunni Iraqis, who make up 20 percent of the population, largely boycotted the elections.
He also said that al-Sistani has endorsed his nomination for prime minister. However, this was not immediately confirmed by al-Sistani's camp.
For the latest news and analysis on Iraq, see RFE/RL's webpage on "The New Iraq".
For news, background, and analysis on Iraq's historic 30 January elections, see RFE/RL's webpage "Iraq Votes 2005".