7 people were killed and at least 30 injured in the explosion at an airport in Burgas, which Bulgarian officials did not confirm as terror-related but which the Israeli prime minister blamed on Iran.
The stepped-up security in New York is precautionary, Browne said.
The daytime bombing killed seven people and injured dozens on a bus full of Israeli tourists on Wednesday.
Bulgarian officials believe it was most likely a suicide attack.
Israel stood by its claim Thursday that Iranian-backed Hezbollah was responsible and vowed to hit back.