By Mohammed Abbas and Sue Pleming

MANAMA (Reuters) - U.S. Secretary of State Condoleezza Rice failed to secure firm commitments on debt relief for Iraq or greater Arab diplomatic representation in Baghdad after a meeting of Arab states on Monday.

But Iraq would now routinely attend some Gulf Arab meetings, which signalled Baghdad's reintegration into regional politics after the U.S.-led invasion in 2003, Rice said after a meeting of the Gulf Cooperation Council plus Jordan and Egypt.

Iraqi Foreign Minister Hoshiyar Zebari, who attended part of the Bahrain meeting after Rice pressed Arab ministers to invite him, warmly embraced his Saudi counterpart and said the atmosphere among neighbours had improved.

"A number of countries around the table talked about their desire of having permanent representation in Iraq," Rice told a news conference. "I do believe that it's a process which will move forward," she said.

Arab states have no permanent representatives in Baghdad and a senior U.S. official who sat in on the meetings said there were no firm commitments yet for opening up embassies.

"But there seemed to be a greater disposition towards it," he told reporters travelling with Rice.

Washington, which accuses Iran of stoking violence in Iraq, has long urged Sunni Arab states to beef up embassies in Baghdad as a sign of support for the Shi'ite-led government and also to counter Iranian influence.

Iraq is a mostly Arab nation while Iran's roots are Persian. Both countries, however, have majority Shi'ite populations.