"That time is now close," Foreign Minister Murray McCully said during the council's open debate on the Middle East, held in New York.
"New Zealand's view on the Middle East peace process has been expressed in this chamber since January. We've made clear that the status quo is unsustainable - doing nothing is not viable. It is encouraging that the Middle East Quartet has re-engaged in capitals on this issue in recent weeks.
"This council must also re-engage. New Zealand has been clear that we see a window of opportunity in the latter part of this year in which the council should act to create a pathway back to the negotiating table and to support the parties once they are there."
Political courage was needed to address that and other "grave issues" in the Middle East, Mr McCully said - and warned the council's credibility was on the line.
New Zealand holds the presidency for the month of July, which means it is chairing all security council meetings and taking a lead on its work on international security issues.
The presidency of the Security Council is shared among all its 15 members on a rotating basis.
"Right across the Middle East, grave issues continue to demand this council's attention," Mr McCully said in his speech.
"The humanitarian situation in Yemen continues to deteriorate. The civil war in Syria rages on. In Iraq, sectarian divides provide space for groups like ISIL to prosper. A basis for lasting peace between Israelis and Palestinians remains elusive."
Against such challenges it was necessary to recognise the breakthrough that the recently struck Iran nuclear deal represented, Mr McCully said.
"At the heart of this diplomatic achievement has been a willingness by the parties to commit to political solutions, and to exercise political courage in the face of significant challenges.
"The question now is whether we can expect to see the same political courage and the same commitment to political solutions brought to the other issues that afflict the region."
Mr McCully said the security council needed to "show some political courage of its own", including on the situation in Syria, which had remained deadlocked for too long.
"The region cannot afford for the conflict to continue. Nor can the council - its credibility is at stake."
Key players in the region, as well as security council members, needed to broker a political solution to the crisis, Mr McCully said.
The humanitarian situation in Yemen continues to deteriorate alarmingly, Mr McCully said, and Iraq faces "ongoing challenges on a number of fronts".
In Libya, an initialling of the Libyan Political Agreement by the Libyan Government and a number of factions was a first step to a lasting peace in the country, Mr McCully said.
By Nicholas Jones of the New Zealand Herald
