The two countries had no relations for nearly two decades, until after another US invasion toppled Saddam in 2003. Iraq then reopened its embassy in Kuwait.
There have been no Arab ambassadors stationed in Iraq since Egypt's envoy was kidnapped and killed shortly after arriving in 2005.
Diplomats from Bahrain, Turkey, the UAE and other Arab countries have all been either killed, wounded or kidnapped in Iraq since 2003.
Washington has been pressing its Arab allies to aid Iraq's recovery by forgiving its debts and restoring diplomatic ties.
In a step toward easing Iraq's regional isolation, the UAE recently waived all of the country's almost $7bn debt and formally appointed an ambassador to Baghdad.
In June, Bahrain said it would set up a new embassy in Baghdad and was selecting an ambassador, although no timeframe was given.
Jordan and Saudi Arabia have also said they planned to open an embassy.
Kuwait's own ties to Iraq are more complicated, as many local residents remain angry about Saddam's 1990 invasion and subsequent occupation of their country.