RIYADH, July 28 (Reuters) - Oman has presented a proposal to Iran for a joint regional mechanism to manage the Strait of Hormuz with voluntary fees, a Gulf source told Reuters on Tuesday.

Under the Omani proposal, which has regional backing, Iran would not exercise sole control of the vital waterway, the source added.

The proposal is based on the Strait of Malacca, where those who use the strait voluntarily contribute to fund navigation, environmental protection and search and rescue.

The U.S. abruptly suspended a ‌campaign of air strikes against Iran over the weekend, raising hopes of a diplomatic solution that would allow shipping to resume in the Strait of Hormuz - which carried a fifth of global energy supplies before the conflict.

President Donald Trump said on Monday the United States was having "good ‌talks" with Iran and there was a chance of a deal, but he warned that U.S. strikes would resume if the negotiations failed to deliver.

Iran's Foreign Minister Abbas Araqchi discussed the Strait of Hormuz with his Omani and Saudi counterparts on Monday.

"He emphasised the need to strengthen cooperation and advance joint diplomatic efforts to establish stability in the region, and lift the insecurity imposed on the Strait of Hormuz due to the aggressive actions of the United States," according to Iran's foreign ministry statement.

(Reporting by Timour Azhari; Writing by Nayera Abdallah, Editing by Andrew Heavens, Kirsten Donovan)