On Wednesday he met with Israeli Prime Minister Benjamin Netanyahu, national security adviser Yossi Cohen and vice prime minister Silven Shalom who is responsible for peace talks with the Palestinians.
Mr Netanyahu raised his concerns over the Iranian nuclear deal.
Mr McCully said he was given a "significant amount of time" by the Israeli leader to explore the Middle East peace process and to get an overview of Israel's concerns.
Earlier this year Mr Netanyahu in a pre-election bid to secure right-wing voters said he no longer supported a two-state solution.
After winning the election he said he would be willing to re-enter peace talks.
New Zealand will make a major push to get Israeli and Palestinian leadership back to the negotiating table this year and has its own resolution.
Mr McCully said he had not seen a French resolution that is believed to push for a two-state solution based on 1967 borders with a strict timeline with talks to be concluded within 18 months.
He said he would let the French resolution takes its course but that New Zealand's own resolution pushing for peace talks would be ready.
"We will give the French proposal a couple of months. There will be a point when the Israeli government is properly formed and the Iranian discussions have concluded.
"This is not a competition, we are in no way motivated to have New Zealand's name on a resolution that goes through the security council on this point, we are simply motivated to see progress made," he said in Jerusalem.
"For us this means creating conditions under which the two principles [Israel and Palestine] can be brought together into a construction dialogue."
Despite his push to see an end to the decades long conflict between Israel and the Palestinians Mr McCully said New Zealand would however not make a move to first recognise the Palestinian state.
Currently 135 of the 195 member states of the United Nations have moved to recognise Palestine as a state.
"We've been very clear with the Palestinians that we're not going to discuss that until after we've exhausted this process.
"We think that we should try and push really hard for direct talks between the parties before complicating that with recognition - but if there's no movement then clearly that's something that us and others in the international community are going to raise."
A Palestinians senior official who did not want to be named disagreed with Mr McCully's unwillingness to recognise a Palestinian state.
"We have a right to self determination and this freedom should not be tied to the negotiations," he said.
PLO spokesman Xavier Abu Eid said New Zealand have a pivotal role to play while on the Security Council and in an ongoing capacity.
"New Zealand has very independent foreign policy and it's strongly rooted in human rights, even though New Zealand might not have the chance to take strong action New Zealand its presence is important."
Mr McCully said New Zealand's good relations with key players were key but it would still be a challenge.
"It probably means striking a position that is equally frustrating and annoying to both of them.
Mr McCully would meet with Palestinian President Mahmoud Abbas and foreign minister Rami Hamdallah today [Middle East Thursday afternoon].