The deal would have let up to 100 British troops stay in Iraq to protect oil platforms and provide training in the south of the country.
The rest of the British forces are withdrawing under a separate agreement.
British Embassy spokesman Jawwad Syed said Tuesday it's a procedural delay and that the remaining British forces will pull back to Kuwait until the issue is resolved.
He says it's a temporary move and that he's optimistic they'll find a way to allow the Britons to return to Iraq.
Iraq's parliament adjourned on Monday for a month-long recess.