The Emirati interior ministry says all legal powers will be used "to respond decisively and without leniency to any actions or attempts that threaten societal stability".
The ministry statement on Sunday did not give details on the suspects or say if they had been charged.
Israeli Prime Minister Benjamin Netanyahu's office had denounced the killing of the rabbi, Zvi Kogan, as a "heinous anti-Semitic terrorist act" and said Israel would do everything it could to bring those responsible to justice.
Prime Minister Benjamin Netanyahu at the Start of the Government Meeting:— Prime Minister of Israel (@IsraeliPM) "The State of Israel will use all means, and will deal with the murderers of Zvi Kogan, and those who dispatched them, to the fullest extent of the law."Full remarks >>https://t.co/U7aV8SNVBf pic.twitter.com/bLMYYlMGumNovember 24, 2024
Kogan was a resident of the UAE and also a Moldovan national, according to local authorities.
He worked with the New York-based Orthodox Jewish Chabad movement and was first reported missing on Thursday. His body was discovered on Sunday.
The Israeli foreign ministry said all Israeli agencies were involved in the investigation and it was believed Kogan had last been seen at a Kosher supermarket in Dubai.
Kogan's body was found in the Emirati city of Al Ain, which borders Oman, though it was not clear if he was killed there or elsewhere, former Israeli politician Ayoob Kara told Reuters in Dubai.
Kara, a member of Israel's ruling right-wing Likud party who promotes economic relations between Israel and the Arab world, said there were indications that investigators suspected Iranian involvement.
The Iranian embassy in the UAE said it "categorically rejects the allegations of Iran's involvement in the murder of this individual".
Israel reissued a recommendation to citizens to avoid non-essential travel to the UAE and said those now there should minimise movement, remain in secure areas and avoid visiting places associated with Israel and Jewish populations.
The UAE's Israeli and Jewish community has grown more visible since 2020, when the UAE became the most prominent Arab state in 30 years to establish formal ties with Israel under a U.S.-brokered agreement, dubbed the Abraham Accords.
The UAE has maintained the relationship during the 13-month Israel-Hamas war in Gaza.
However, Israelis and Jews have been less evident in public since the devastating Hamas attack on Israeli communities of October 7, 2023 that triggered the Gaza conflict, which has sparked protests worldwide.