The government machinery pounced swiftly.

Ten of the signatories were detained on Monday, and another four were ordered to report to the police but were not jailed in view of their advanced years. Mr. Erdogan accused them of plotting a coup, a toxic allegation after four years of thousands of detentions and purges since the last failed coup. Some saw that as a warning to serving officers who might have similar thoughts.

Mr. Erdogan had “got his groove back” Steven A. Cook, a senior fellow for Middle East and Africa Studies at the Council on Foreign Relations in New York, wrote in an analysis.

The admirals’ letter did not come out of the blue. A year earlier, 126 retired Turkish diplomats had penned an open letter warning against withdrawing from the convention. The debate reveals the deep divisions between secularists and Islamists that have been tearing Turkey apart since Mr. Erdogan’s rise to power in 2002.

Caught up in their own dislike of the secular republic that replaced the Ottoman Empire, the Islamists distrust the Montreux Convention, said Asli Aydintasbas, a senior fellow with the European Council on Foreign Relations. That was an erroneous reading of history, she added, but Mr. Erdogan feels that the convention needs “to be modernized to meet Turkey’s new coveted role as a regional heavyweight.”

Secularists, as well as most Turkish diplomats and foreign policy experts, see the Montreux Convention as a win for Turkey and fundamental to Turkish independence and to stability in the region.

Russia would have most to lose from a change in the treaty, said Serhat Guvenc, a professor of international relations at Kadir Has University in Istanbul, although any alteration or break up of the convention seems inconceivable, since it would demand consensus from the multiple signatories.

“Russia would resent it and be provoked,” he said. The United States and China would gain, since neither currently is allowed to move large warships or aircraft carriers into the Black Sea.

Most analysts said that Mr. Erdogan and his advisers knew the impossibility of changing the Montreux Convention, but that the veteran politician is using the issue to kick up a storm.

“It is the government’s way of lobbying for the canal,” Ms. Aydintasbas said. “Erdogan is adamant about building a channel parallel to the Bosporus, and one of the government’s arguments will likely be that this new strait allows Turkey to have full sovereignty — as opposed to the free passage of Montreux.”

That interpretation is both inaccurate and dangerous, she said. “Inaccurate because as long as Montreux is there, no vessel is obliged to use the new canal. Dangerous because it could aggravate the Russians and the international community.”

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