The twin attacks in Istanbul on Saturday - involving a suicide bomber on foot and another in a car - killed 44 people, mostly policemen, outside Besiktas soccer stadium, and injured more than 150.
Earlier this week, Turkish police carried out a series of raids and detained 568 people over alleged links to Kurdish militants, intensifying a crackdown after the bombings.
An offshoot of the militant Kurdistan Workers Party (PKK) claimed responsibility fir attacks on Saturday night.
"We are always telling our counterparts that we are receiving this threat. And now, we see that the Besiktas bomber also came from Syria," Cavusoglu told TGRT TV in an interview. He did not say which of the Besiktas bombers he meant.
Turkish authorities consider the Democratic Union Party (PYD) and its armed wing, the YPG, to be the Syrian offshoots of the PKK, which has waged a guerrilla war for autonomy in the mainly Kurdish southeast of Turkey for decades.
Turkey is frustrated with international support for the YPG, which is fighting Islamic State militants in Syria.
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Members of the pro-Kurdish Peoples' Democratic Party (HDP), parliament's second-biggest opposition grouping, have been among those arrested since the attack, the Interior Ministry said.
President Tayyip Erdogan has accused the HDP of links to the PKK. The HDP, which last year became the first Kurdish party to enter parliament, denies direct links to militants.
The PKK, which took up arms in 1984, is deemed a terrorist organization by the United States and European Union, as well as by Turkey. Saturday's attack was one of the deadliest claimed by Kurdish militants for decades.
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