The visit comes days after an Indian warship anchored at Israel's Haifa port.
During their five-day stay in Iran, the ships will hold various interactions with their Iranian Navy counterparts and joint exercises at sea.
The visit would also include training and sports events between the two navies.
This deployment would add another chapter to the cordial relations and defence cooperation between India and Iran, an Indian Navy statement said.
The 125-metres long ships displace 3,600 tonnes and are capable of operating at extended ranges, with speeds up to 30 knots.
They have state-of-the-art sensor suites and an impressive weapon package, including long range surface-to-surface missiles and anti-missile defence systems.
Their combat capability is further augmented by the capability to embark two multi-mission capable Seaking helicopters.
The ships have completed over a decade of service with the Indian Navy. INS Betwa is presently commanded by Captain KM Ramakrishnan and INS Beas is commanded by Captain Deepak Bhatia.
"It has been India's national objective to ensure a secure and stable regional environment, which is conducive for economic and social development not just at home, but also in immediate and extended neighbourhood.
"The Indian Navy, while shouldering its security responsibilities, is committed to these objectives and has been contributing towards humanitarian assistance, capacity building and capability enhancement of friendly foreign countries when so needed," the statement said.
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