DUBAI, July 28 (Reuters) - Iran has proposed to Oman a temporary arrangement to reopen the Strait of Hormuz under which one direction of traffic would pass through Iranian waters and part of the opposite route would also be in Iranian waters, Deputy Foreign Minister Kazem Gharibabadi told state television on Tuesday.

Gharibabadi said Tehran rejected an Omani proposal for an equal division of transit routes between the two countries, saying such a plan did not address Tehran's security concerns until long-term regional stability is achieved.

He said the Strait of Hormuz would remain closed if Muscat rejected Iran's proposal, adding that Tehran had never recognised the southern route along Oman's coast.

Gharibabadi also said Tehran had made it clear to Muscat that it no longer recognised the Traffic Separation Scheme (TSS), arguing that this pathway roughly in the middle of the waterway lies mostly within Omani waters and runs contrary to Iran's need to monitor transiting vessels after being attacked by the U.S. and Israel in late February.

The TSS, adopted by the International Maritime Organization, is currently unusable due to the risk of mines and has been replaced with Iran's northern route and Oman's southern route.

"This is for national security and not bullying because when the TSS was for 60 years in Omani waters, we didn't say anything," Gharibabadi said.

The Iranian diplomat also warned that Tehran would not allow any third country, even if invited by Oman, to de-mine the Strait of Hormuz.

(Reporting by Dubai Newsroom; Editing by Hugh Lawson and Rod Nickel)