By Laurence Norman 

NEW YORK--The first full round of nuclear talks between Iran and six world powers resumed Friday in New York after a two-month gap, with Western officials saying the coming days are critical to reaching a deal by the Nov. 24 deadline.

The talks are taking place to the backdrop of the annual United Nations General Assembly meeting, meaning leaders and foreign ministers from Iran and the six powers will be in town.

Western officials say they hope that will inject some needed momentum into discussions and help them answer their biggest question of whether Iran's negotiating team has political cover to accept a major cut in Tehran's current nuclear-enrichment program under a final deal.

"We are entering the crucial phase of the...negotiations with Iran," German Foreign Minister Frank-Walter Steinmeier told reporters Friday. "There is no more room for Iran to play for time. We are willing to offer Iran a fair deal. However for that to happen, Iran will need to move on the core issues."

The mood coming into this week's talks was anything but buoyant. It has been 10 months since Iran and the six powers reached a historic interim deal curbing the most advanced parts of Iran's nuclear activities in exchange for modest sanctions relief.

The two sides missed a July 20 target date for a final deal and bilateral summer talks between Iran and the U.S. made scant progress, diplomats said. In recent weeks, Tehran and Washington have scrapped over new U.S. sanctions on Tehran and over U.S. efforts to build an international coalition against Sunni extremist group Islamic State without Iran's direct participation.

Iran, which insists its nuclear program is for purely peaceful civilian purposes, negotiates with the U.S., U.K., France, Germany, China and Russia, the so-called P5+1 Group.

A comprehensive deal would commit Iran to take clear steps to significantly curtail its nuclear program in exchange for gradual sanctions relief.

"Coming into New York, I think many of us were not very optimistic," a senior U.S. official said Thursday. "But clearly, over meetings over the last two days both with Iran and with my P5+1 and EU colleagues, it is clear that everyone has come here to go to work."

Speaking in New York on Wednesday evening, Iran's Foreign Minister Javad Zarif said his side was "committed to resolving this issue." But Mr. Zarif said Iranian trust in U.S. intentions remained low. A senior Western diplomat who visited Tehran recently said top Iranian officials were pessimistic about a deal, openly questioning Washington's desire for an agreement.

Gaps have narrowed, but not closed, on a range of issues including a future inspections regime under a nuclear deal, the final design of Iran's heavy water reactor in Arak and the future of Iran's underground Fordow nuclear site.

However, the two sides remain openly at odds over the slow pace of Iran's explanations of its past nuclear activities and over the duration of a nuclear deal. However the sharpest difference is over the caps a nuclear deal would place on Iran's future enrichment program.

In July, Iranian officials said they were prepared to maintain or modestly reduce their current enrichment program under a final deal but Western officials say it should be sharply reduced.

"The Iranians have said over these many days and weeks how reasonable and flexible they are...and about how their current capacity should be acceptable," the senior U.S. official said. "But the status quo is not doable for any of us."

The official said the six power group has been offering "creative solutions" over the summer but that Iran hadn't been immediately responsive.

"There is a unique opportunity over this next week and a half when heads of state, foreign ministers...are gathered in New York," the official said. "There is an opportunity to... see whether the outlines, and...the details of a potential agreement begin to emerge."

A second western diplomat said there were signs in bilateral talks this week that Iran realized it must show more flexibility on enrichment. But the official said it remained unclear whether they could "significantly narrow the gaps" during the New York talks.

Friday's talks started with a brief meeting of top negotiators from Iran and the P5+1 at the U.N. There will be a mix of bilateral and multilateral meetings in coming days at expert and senior official levels.

Foreign ministers are likely to meet although that hasn't been confirmed. U.S. President Barack Obama is "open to" meeting with Iranian President Hasan Rouhani, the senior U.S. official said Thursday, but nothing is yet planned. At last year's general assembly, the two leaders held a historic phone call but didn't meet.

Write to Laurence Norman at laurence.norman@wsj.com

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