Ibrahim al-Jaafari was speaking to reporters on Monday in Najaf after meeting Grand Ayatollah Ali al-Sistani, Iraq's most revered Shia cleric and the patron of the country's Shia political parties.
Replying to a reporter's question, al-Jaafari said: "Those who have objections against me should present their reasons. We have been elected by the people."
He said the formation of a new government faced obstacles, but not insurmountable ones.
Al-Jaafari hopes to have a national unity government that groups his Shia alliance, Kurdish parties and two Sunni groupings that won a total of 55 seats in the election on 15 December.
He said he hoped the formation of the government would not take as long as it did last time, when his first government took office three months after the previous general election on 30 January 2005.
Sunni Arabs are demanding that the next government's decisions be made by consensus and seeking assurances that clauses they object to in a new constitution will be amended. These clauses are to do with federalism, the identity of Iraq and the drive to rid the government of former senior members of Saddam Hussein's Baath Party.
The Sunnis see "de-Baathification" as an excuse to hound members of their community out of government jobs.
Al-Jaafari, who first came to office in April, won the nomination of the largest parliamentary bloc last week. The Shia United Iraqi Alliance has 130 of parliament's 275 seats and its nominee for prime minister should be assured of getting the job.
Al-Jaafari beat his heavily favoured rival Adil Abdul-Mahdi, the Vice-President, by a vote in a stunning coup that has jolted the political scene in Iraq.