Addressing the Security Council on the eve of talks in Cairo between Palestinian factions, UN envoy Nickolay Mladenov said the Egyptian-led "process must not be allowed to fail."
"If it does, it will most likely result in another devastating conflict," warned Mladenov.
"Whether it would be triggered by a meltdown of law and order in Gaza, by the reckless action of extremists or by strategic choice, the result will be the same - devastation and suffering for all."
Hamas, the Islamist movement that has ruled Gaza since 2007, and Israel have fought three wars since 2008, the last conflict dating back to 2014.
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Under the unity deal signed last month, the Palestinian Authority is to resume full control of the Gaza Strip by December 1.
At the weekend, the Rafah border crossing between Egypt and Gaza was reopened after the Palestinian Authority took control of the crossing for the first time since 2007.
"After living in abject misery under Hamas control and locked in by the closures, their situation is close to exploding."
Israel however has reacted coolly to the deal, saying it will not negotiate with a government that includes Hamas if the Islamist movement does not disarm.
Mladenov also expressed concern about a row between the United States and the Palestinian Liberation Organization over the PLO's office in Washington.
The US State Department has refused to renew the permission for the PLO office to operate in Washington, prompting PLO leaders to threaten a freeze on ties with the US administration.