BAGHDAD , Iraq -LRB- CNN -RRB- -- Iraq 's main political parties Sunday reached a deal designed to allow non-U.S. foreign troops to stay in the country past the end of the year , when a United Nations resolution authorizing their presence expires . Iraqi and British soldiers during an Iraqi army training session in Basra last week . The deal would set a deadline of July 31 , 2009 , for all non-U.S. foreign troops to withdraw , according to Abdul Hadi al-Hassani , a lawmaker with the main Shiite parliamentary bloc , who spoke to Iraqi state television on Sunday . The agreement awaits approval by Iraq 's Parliament , which is expected to vote on the measure on Monday , several Iraqi lawmakers said . The emergency negotiations came after lawmakers Saturday rejected a similar proposal that would have been law . Sunday 's proposal , by contrast , was drafted as a resolution that would empower the Cabinet to authorize international troop presence without requiring Parliament to pass a law . Washington and Baghdad have already worked out a separate agreement that will keep U.S. troops in Iraq but tighten restrictions on them . Countries other than the United States that have troops in Iraq could be left with no legal cover for their presence there if Baghdad does not act swiftly . Iraq 's Cabinet had approved a draft law authorizing non-U.S. foreign troops Tuesday , the first step in passing legislation , but it fell at the next hurdle -- Parliament . That left lawmakers scrambling Sunday for a way to give foreign troops legal cover quickly . Lawmakers expect Sunday 's agreement to cut through the problem , because a resolution can be passed in a single day , while it takes at least a week to pass a law . British government lawyers , meanwhile , are studying `` all possible options '' to legally extend the presence of British troops in Iraq beyond New Year 's Day in case Iraq 's Parliament rejects the new compromise . Britain has the second-largest contingent of foreign troops in Iraq -- about 4,100 -- after the United States , which has about 142,500 . All other countries combined have only several hundred troops in the country . Britain and Iraq announced last week that British troops would begin leaving Iraq in May 2009 , while a `` handful '' of British military personnel would remain after that date to continue naval training for Iraqi sailors , primarily to protect oil platforms . The United States reached a security agreement with Iraq in November . That deal , which was ratified by the Iraqi Parliament , calls for American troops to leave Iraqi cities by June 2009 , and to be out of Iraq by the end of 2011 . Beginning New Year 's Day , U.S. commanders will have to get prior Iraqi government approval for any operations . American military personnel who commit crimes while not on duty or who commit grave crimes while on duty would be subject to Iraqi legal jurisdiction under the new agreement . The U.S. security agreement does not govern the presence of troops from other coalition countries . The Parliament 's rejection of the Cabinet 's proposed law allowing foreign forces to remain in Iraq after January 1 came after heated arguments that lasted for days . The session became so contentious that Parliament 's speaker threatened to resign , lawmakers said . Some political blocs , notably the Sadrists , oppose any extension of the presence of foreign troops in Iraq . That group , headed by Shiite leader Muqtada al-Sadr -- an anti-Western cleric -- is demanding an immediate withdrawal of foreign forces . CNN 's Jill Dougherty and Jomana Karadsheh contributed to this report .