By Fredrik Dahl

VIENNA (Reuters) - Iran will cooperate with the U.N. nuclear agency to find ways to "overcome existing issues once and for all", Tehran's new envoy said on Thursday, hinting at a more flexible approach under relatively moderate President Hassan Rouhani.

But Ambassador Reza Najafi, at his first board meeting of the International Atomic Energy Agency (IAEA), also repeated Iran's stance that it would not cede what it calls its legitimate right to a peaceful nuclear energy program.

"Based on its rights and obligations recognized under the NPT (Non-Proliferation Treaty), Iran is ready to faithfully engage and remove any ambiguity on its nuclear activities," Najafi told the 35-nation governing board of the IAEA.

Iran is at odds in particular with Western powers, which fear its nuclear program is covertly directed at giving it the means to build nuclear bombs. Tehran denies this and rejects any limits on its enrichment of uranium or a more intrusive IAEA inspection regime, sought in several U.N. resolutions.

Separately from big power diplomacy to resolve a decade-old dispute that could yet trigger a Middle East war, the IAEA has held 10 rounds of talks with Iran since early 2012 in a bid to resume a blocked inquiry into suspected atom bomb research.

The talks have so far yielded no results but Western states see a meeting set for September 27 in Vienna as a litmus test of any substantive Iranian shift from its intransigence under Rouhani's hardline conservative predecessor, Mahmoud Ahmadinejad.

Israel - widely believed to be the Middle East's only nuclear-armed power - made clear its deep skepticism about any change in Tehran's policy as a result of Rouhani's election.

"Iran is leading the agency and the entire world community around in circles," Ambassador Ehud Azoulay told the IAEA board.

Najafi, appointed as Iran's ambassador to the IAEA after Rouhani took office on August 3, cited a strong political will on Tehran's part to "constructively interact" on the nuclear issue.

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"We are looking forward to working closely with the Director General (Yukiya Amano) and his team in the coming days," the soft-spoken career diplomat and disarmament expert said.

"NO LANGUAGE OF THREAT"

Asked whether he was hopeful that an agreement could be reached in the Vienna meeting, he later told a brief news conference: "We sit together, we directly and frankly discuss the differences. We hope that we can solve those differences."

Western diplomats welcomed his conciliatory tone but cautioned it remained to be seen whether there would also be a change in substance following the June election of Rouhani.

They said Najafi's remarks - though short on specifics - were more matter of fact than those of his predecessor, Ali Asghar Soltanieh, who often used IAEA board meetings to rail against Tehran's Western foes and the U.N. nuclear agency.

Iran says it is enriching uranium only for civilian energy and medicine, denying any aim to acquire nuclear weapons.

Rouhani, who has vowed that Iran will be more transparent and less confrontational in talks both with the IAEA and the big powers, said this week that time for resolving Iran's nuclear dispute with the West was limited.

He said he would meet foreign ministers of some of the six powers - Russia, China, France, Britain, the United States and Germany - when he attends the U.N. General Assembly in New York this month.

A senior adviser to Russian President Vladimir Putin, who is expected to meet Rouhani on Friday, told reporters Moscow hopes that new talks between Iran and the six powers will be held very soon and that both sides need to be flexible. Russia has much warmer ties with the Islamic Republic than Western states do.

"It is important that Iran display the necessary flexibility and readiness to meet the international community's demands," Yuri Ushakov said. "The six nations, in turn, should also demonstrate a creative approach and be ready to respond adequately to the positive steps that we expect from Iran."

Western powers, which have imposed toughening sanctions on Iran over the last few years, say they hope that the election of Rouhani will lead to a softening of Tehran's approach.

But they stress that there is as yet no sign of Iran slowing its nuclear program. On the contrary, Western diplomats say, Iran has continued to expand its uranium enrichment capacity in recent months, potentially shortening the time it would need to produce sufficient highly-refined material for a bomb.

(Additional reporting by Alexei Anishchuk in Moscow,; Editing by Mark Heinrich and Paul Taylor)