BAGHDAD, Feb 3 (Reuters) - Iraq's presidency council said on Sunday a measure that would give thousands of former members of Saddam Hussein's Baath party their old jobs back had become law, despite objections from one of the country's two vice presidents.

Parliament passed the "Accountability and Justice Law" last month, winning praise from Washington for helping promote reconciliation between majority Shi'ites and minority Sunni Arabs who were dominant under Saddam.

A statement from the presidency council said the measure had become law.

The council consists of President Jalal Talabani, a Kurd, Sunni Arab Vice President Tareq al-Hashemi, and Shi'ite Vice President Adel Abdul-Mahdi.

Hashemi said late last week he would not back the legislation because it would force many people given jobs after the 2003 U.S.-led invasion out of those posts.

(Reporting by Wisam Mohammed, Writing by Michael Holden, Editing by Dean Yates)

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