The draft describes US-brokered talks between Israelis and Palestinians as "irreversible" and urges greater diplomatic efforts to secure a deal.
The resolution is the first on the Middle East issue adopted by the 15-member council in almost five years.
It passed by 14 votes to zero. One council member, Libya, abstained.
The draft calls on both parties to "refrain from any steps that could undermine confidence or prejudice the outcome of negotiations".
It also urges an "intensification of diplomatic efforts" to build lasting peace in the Middle East.
The US-brokered negotiations were launched at Annapolis, Maryland, in November 2007, with the goal of achieving a peace deal before President George W Bush leaves office on 20 January 2009.
This is not going to happen but, says the BBC's Laura Trevelyan at the UN, the resolution gives the security council's backing for the talks to continue.
Diplomats say the resolution is America's attempt to carry over any progress to Barack Obama's administration.
Polls suggest the hawkish Binjamin Netanyahu could be elected Israeli prime minister in February, however, and he does not want to carry on with the negotiations in their current format, our correspondent adds.
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