There was no comment on the announcement from Zalmay Khalilzad, the US ambassador, or Talabani, and Barzani did not elaborate.
It was unclear whether new concessions had to be made to win his approval.
After the cabinet signs off, the measure goes to parliament for final approval once the legislators return from a recess early next month.
Analysts believe that a new law is needed to encourage international companies to invest in Iraq to repair pipelines, upgrade wells, develop new fields and to exploit the country's vast petroleum reserves, which is estimated at about 115bn barrels.
According to Iraqis familiar with the deliberations, the draft law would offer international oil companies several methods to invest, including production-sharing agreements.
The agreements would give US and other international companies a substantial share of the oil revenues to recover their initial investments and then allow them big tax breaks.
That angers some Iraqis, who believe foreign investors will get too much control of the nation's wealth.
But the biggest battle is over who gets the most say in awarding contracts and managing the revenues. The Kurds, who have run their own mini-state in the north since 1991, want regional administrations to have a bigger role.
Most of the country's proven oil reserves lie in the Kurdish north and the Shia-dominated south, which also wants to establish a self-ruled region.
That has led the Sunni Iraqis to demand more power for the central government, to assure them a share of the wealth.
To win Kurdish approval, the current draft gives a major role to the regional administrations in awarding contracts but allows a committee under the prime minister to review them.
To satisfy Iraqi Sunnis, oil revenues would be distributed to the 18 provinces based on their populations - not on whether they have oil.
While the Kurds want more control of revenue generated from their fields, others think the new proposals give the regions too much control.
Speaking at an oil seminar in Jordan this month, Tariq Shafiq, a former oil official, who helped draft the first version, said: "If implemented, the balance of power in the management of Iraq's oil and gas resources would have shifted alarmingly from the centre to the regions."
In a related development, Hussein al-Shahrastani, Iraqi oil minister, has announced a 15 per cent increase in fuel prices to be applied as early as March.
Al Shahrastani said that the decision was made after consultation with the International Monetary Fund to lift subsidies on fuel products.
The government plans to raise the price of benzene to 400 dinars a gallon and petrol to 350 dinars a gallon.