Authorities said one of the men was arrested Wednesday at Kennedy Airport, where he was attempting to board a flight to Istanbul.
A second suspect was arrested in Brooklyn and a third in Florida.
They are charged with attempt and conspiracy to provide material support to a terrorist organization.
De Blasio said the working relationship between the city and the federal law enforcers who arrested the men is “very, very close.”
He added that the city would deepen its “anti-terrorism capacity.”
De Blasio spoke in Albany, where he testified before state legislators about the city’s budget needs.