"I call on all our partners in the political process and in this national unity government to respect this deal."
Iraq's Sunnis live mainly in central provinces that have little proven oil wealth, and they fear they will not benefit from oil profits should violence ease enough to revive the struggling industry.
The draft oil law was originally approved by the cabinet in February but faced opposition from the government in autonomous Kurdistan.
Besides deciding who controls the country's oil reserves and setting up a new oil firm to oversee the industry, the law aims to provide a legal framework for attracting foreign investment.
Other major laws also need to be passed that set provincial elections by the end of the year and that allow some members of Saddam Hussein's Batath party to return to government and the military.
Al-Maliki said these laws would be discussed next week.
Clock ticking
Parliament is running out time to debate and approve the series of laws.
It has already extended its current session till the end of July, before legislators take a month off.
That leaves little time for General David Petraeus, the US military commander in Iraq and Ryan Crocker, the US ambassador, before they present a report to Washington on Iraq's security and political progress - due mid-September.
The report is being viewed as a political watershed, with George Bush, the US president, under mounting pressure to show his Iraq strategy is working and with campaigning in the 2008 US presidential race already well under way.