ANKARA, July 4 (Reuters) - Turkey's armed forces command said on Wednesday it had found the bodies of both pilots of an F-4 jet shot down by Syria last month and was trying to retrieve them from the seabed.

Relations between Ankara and Damascus hit a new low after Syria shot down the Turkish reconnaissance plane over the Mediterranean on June 22, prompting a sharp rebuke from Turkey, which said it would respond "decisively".

Syria says it downed the jet in self-defence when it was inside Syrian airspace. Turkey says the plane accidentally violated Syrian airspace for a few minutes but was later brought down in international airspace.

The military has been searching for the pilots and this week brought in a specialised ship to recover the wreckage of their plane, some 1,000 metres (3,300 feet) underwater.

It named the pilots as Air Force Captain Gokhan Ertan and Air Force Lieutenant Hasan Huseyin Aksoy. The military did not specify where the bodies were found, but there has been no report that the pilots ejected from the plane.

Turkey has heightened military activity along its border with Syria since the incident and scrambled F-16 fighter jets on three consecutive days in the past week after it spotted Syrian transport helicopters flying near the Turkish border.

Ankara has said the shooting down would not go "unpunished" and summoned a meeting of its NATO allies shortly after the incident, but it has not retaliated. Both Syria and Turkey have said they do not want the incident to lead to an armed conflict.

In an interview with Turkish paper Cumhuriyet published on Tuesday, Assad said he wished his forces had not shot the jet down, repeating Damascus's position they had not known the identity of the plane at the time.

Turkey dismisses this assertion, saying the plane was unarmed, was not hiding its identity and was attacked without warning. (Writing by Jonathon Burch; Editing by Alistair Lyon)