By Gram Slattery and Timour Azhari ABU DHABI, June 23 (Reuters) - U.S. Secretary of State Marco Rubio faces a delicate mission this week pitching Washington's Iran peace deal to Gulf Arab leaders who fear excessive concessions will strengthen Tehran and reshape the region's security balance and oil flows. Rubio will meet them in the United Arab Emirates on Tuesday, before traveling to Kuwait and Bahrain, where he will meet officials from the Gulf Cooperation Council, a grouping of monarchies that also includes Saudi Arabia, Qatar and Oman.