Nickolay Mladenov, the UN special Middle East coordinator, told the Security Council that "the coming period will be critical to the future of the peace process."
Peace talks between Israel and the Palestinians have been comatose since a major US push for a final deal ended in failure in April 2014.
UN efforts to revive the peace process were effectively on hold in recent months as Israel held elections and Prime Minister Benjamin Netanyahu formed a new government that was announced last week.
Mladenov said he and UN Secretary-General Ban Ki-moon "will be engaging the new government to explore realistic options for a return to meaningful negotiations towards a two-state solution within a reasonable timeframe."
The envoy, who took up his post last month, renewed a UN call for a freeze on Israeli settlement activity and urged the new government to reverse decisions on three recent tenders for new construction.
The United Nations has repeatedly called on Israel to halt the construction of Jewish settlements on Palestinian land, which it has branded as illegal and a move to erase the prospect of a Palestinian state.
"To give hope back to people, we must act to advance the prospect of a two-state solution: Israel and Palestine living side-by-side in peace and security," Mladenov told the 15-member council.
Mladenov's predecessor, Dutch diplomat Robert Serry, told the Security Council in March that the settlements were threatening to "kill the very possibility of reaching peace."
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Serry said in his final report to the council that he was unsure whether it was "already too late."
- Security Council resolution -
The UN push to put peace talks back on track comes amid discussions at the Security Council on a possible draft resolution that would outline the parameters of a final deal.
The draft resolution would pave the way for a Palestinian state encompassing the West Bank and Gaza, with a shared capital in Jerusalem, and set a deadline for ending negotiations.
Following heavy US lobbying, the council in December rejected a similar draft proposed by Arab countries but France has said it would be willing to try again.
France, however, has not circulated a draft and diplomats have suggested that negotiations on a text would have to wait until after work on finalizing the Iran nuclear deal is completed in June.
This would give the United States, which voted against the resolution in December, more leeway to engage with France on a text that it could ultimately support at the council.
The US administration has not, however, said whether it would be prepared to endorse a UN resolution on a final Israeli-Palestinian peace deal.
International concern over the peace process spiked after Netanyahu vowed during an election campaign speech that he would never allow the creation of a Palestinian state, although he later backtracked on his comments.