National police chief Khalid Abu Bakar tweeted that Turgay Karaman and Ihsan Aslan were arrested "because they threatened the security of Malaysia." No further details were provided by authorities and the Turkish embassy refused to comment.
Turkey detains 35 suspected Islamic State members in Istanbul
Local media reports had been circulating allegations that both men had been abducted.
Another Turkish national Suheyl Ozcelik on Tuesday lodged a police report saying he had seen CCTV footage of five men abducting Karaman, a physics teacher, at a Kuala Lumpur carpark.
"The CCTV recordings clearly showed the faces of these five unknown men who blocked Mr Turgay's (Karaman) face from the camera," he said in the police report seen by AFP.
Ozcelik also said two of his Turkish friends were abducted last year and deported to Turkey. "I am very afraid for my safety and scared that my Turkish friends who are kidnapped and sent to Turkey will be tortured and killed," he said in his police report, without indicating possible reasons.
Media reports say the other arrested Turk, Ihsan Aslan, is a businessman.
Phil Robertson, deputy Asia director at Human Rights Watch, said the national police chief should grant the two men immediate access to their lawyers and families and give details of how they posed a threat to Malaysia. He said Malaysia should not become "a handmaiden to Turkish repression".
"They should not be taking the word of the Turkish government as their only source of information on Turkish nationals overseas," Robertson told AFP.
Turkey detains more than 2,000 people over militant, coup links - interior ministry
"The Turkish government is on a witch hunt against the perceived enemies of President Erdogan."
Erdogan's government has detained or sacked tens of thousands of people under a state of emergency imposed after last year's failed coup. The crackdown focuses on alleged supporters of the US-based preacher Fethullah Gulen, blamed for the failed coup.
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