One of the men, Volodymyr Lisovyi, said he was aware of the “provocative nature” of the Ukrainian action.
Ukraine’s navy commander said the men had been forced to lie under duress.
Meanwhile, a Crimean court ordered that 12 of the 24 Ukrainians seized on Sunday be detained for 60 days.
Ukraine and Russia accuse each other of violating international maritime law. They refer to the 1982 UN Convention on the Law of the Sea, which both states joined in the 1990s.
Ukraine insists on freedom of movement in the Kerch Strait and the Sea of Azov in accordance with this agreement, while the Russian side is trying to draw territorial borders. The countries also have a bilateral agreement on the free use of the Kerch Strait and the Sea of Azov, an accord that Russia has never called into question.
The Kerch Strait is the only connection between the Black Sea and the Sea of Azov, and the only way to reach two important Ukrainian ports, Mariupol and Berdiansk. Russia has controlled the strait since annexing Crimea in 2014, which has made traffic significantly more difficult for Ukrainian ships.
About the Sea of Azov: It is a sea in Eastern Europe. To the south, it is linked by the narrow (about 4 km or 2.5 mi) Strait of Kerch to the Black Sea, and it is sometimes regarded as a northern extension of the Black Sea.
The sea is bounded in the north and in the west by Ukraine, in the east by Russia.
The Don and Kuban are the major rivers that flow into it.
The Sea of Azov is the shallowest sea in the world, with the depth varying between 0.9 and 14 meters.