Hussain al-Shahristani, who was attending an oil conference in Dubai, the United Arab Emirates, did not give a specific day but said the measure would go to lawmakers before the next week was out.
In Baghdad, oil ministry spokesman Assem Jihad told The Associated Press in a telephone interview that the draft law would be in front of the legislature "within the coming few days if everything goes well."
"The draft is with the State Shura Council now to be put in a legal form after being written in technical language," Jihad said.
"We are expecting to take no more than two months to discuss it inside the parliament... between one and two months it depends on the parliament," Jihad added.
The Iraqi oil legislation, which was endorsed by the cabinet last February, will open the door for the government to sign contracts for exploration and production of the country's vast untapped reserves.
It was designed to create a fair distribution of oil profits to all Iraqis and it is perhaps the most important piece of legislation for Iraq's American patrons.
Passage of the law, thought to have been written with heavy U.S. involvement, is one of four benchmarks the Bush administration has set for Prime Minister Nouri al-Maliki's struggling government.
But the oil minister of Iraq's Kurdish regional government said the country should revise the draft law to encourage more competition and investment in the oil and gas industry.
"We are broke. Nobody is going to lend Iraq any new money to invest in its old, lousy oil fields. We have to do these professionally and on a competitive basis," Ashti Abdullah Hawrami told Dow Jones Newswires at the Dubai meeting.
He also said proposals to the draft law that would give the Iraqi National Oil Co. control over 90 percent of the country's oil reserves threaten the law's approval.
Iraq sits on 115 billion barrels proven oil reserves which make it the world's third-largest, but Iraq has lagged in exploration technology.
Meanwhile, CBS News reporter Larry Miller reports that Iraqis could be sitting on nearly twice as much oil as previously thought, according to a comprehensive new geological study.
A report in Thursday's Financial Times says there could be 100 billion barrels in Iraq's western desert region that no one knew about.
If accurate — and the country's violent conflict can be resolved — Iraq would leapfrog Iran and become the world's second largest oil producer, behind Saudia Arabia, reports Miller.
Currently, only one third of Iraq's oilfields are productive. Oil officials say around $25 billion in foreign investment is needed to reach full potential.
Iraq exports about 2 million barrels of oil every day, of which about 1.6 million barrels are exported through the port of Basra and some 300,000 are pumped from the northern city of Kirkuk to the Turkish port of Ceyhan.
Oil production has plummeted since the U.S.-led invasion in March 2003 as the oil pipelines have faced repeated insurgent sabotage, attacks on maintenance crews, alleged corruption, theft and mismanagement.