* Kerry meets with Iran's foreign minister, other envoys
* Britain, France, Russia, China, Germany also in meeting
* Rouhani says no nation should possess nuclear arms
UNITED NATIONS, Sept 26 (Reuters) - Iran and the United States held their highest-level substantive talks in a generation on Thursday, saying the tone was positive but sounding cautious about resolving the long-running standoff over Iran's nuclear program.
U.S. Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif met after the Iranian held wider talks with the United States and other major powers to address Western suspicions Iran may be trying to develop atomic weapons.
Diplomats from the major countries described the atmosphere of the wider talks in positive terms but they, as well as the U.S. and Iranian foreign ministers, stressed the difficulty of resolving a dispute that has eluded solution for a decade.
"We had a very constructive meeting," Kerry told reporters at the United Nations, where he and Zarif sat next to one another in a gesture that suggested a desire on both sides to explore how to ease their nations' more than three-decade estrangement.
The United States wants Iran to address questions about its nuclear program, which Washington and its allies suspect is a cover for developing nuclear weapons. Iran denies this, saying its program is for solely peaceful, civilian uses.
"Needless to say, one meeting and a change in tone, which was welcome, doesn't answer those questions yet and there is a lot of work to be done," Kerry told reporters.
Zarif also sounded a cautionary note.
"I am satisfied with this first step. Now we have to see whether we can match our positive words with serious deeds so we can move forward," he said.
Kerry said Zarif had put some "possibilities" on the table, but stressed that there was more work to be done. Zarif, meanwhile, insisted on quick relief from economic sanctions that have damaged Iran's economy.
Kerry and counterparts from the five permanent members of the U.N. Security Council and Germany described their meeting with Zarif on the sidelines of the U.N. General Assembly as "a change in tone" from encounters with Iran's previous, hardline government.
European Union foreign policy chief Catherine Ashton, who chaired the meeting, told reporters it had been "a substantial meeting. Good atmosphere. Energetic."
She said the two sides had agreed on an "ambitious timetable" to address Western concerns about Iran's nuclear program and would meet again in Geneva on Oct. 15-16 "to pursue the agenda to carry on from today's meeting and to hopefully move this process forward."
Ashton also added a note of caution, saying it was important to focus on "effective work that we do on the ground."
HANDSHAKE OR NO HANDSHAKE
It was a very uncommon encounter between top officials of the United States and Iran, which have been estranged since Iran's 1979 Islamic Revolution toppled the U.S.-backed shah. It was the first meeting between a U.S. secretary of state and an Iranian foreign minister since a brief encounter in May 2007.
Kerry was seen smiling at Zarif at the start of the meeting and Ashton hinted that he and Zarif shook hands, noting that the two had sat side-by-side.
"Secretary Kerry ... is a man of great politeness, so it would be surprising if they didn't do that," she said.
"We all shook hands and we all smiled," said Chinese Foreign Minister Wang Yi after the meeting on Iran.
The New York talks involved the five permanent members of the U.N. Security Council - Britain, France, Russia, China, the United States - and Germany, known as the P5+1.
Ahead of the talks, Kerry said he looked forward to a "good meeting" - the first involving the newly elected Iranian government of centrist President Hassan Rouhani - but would not specify what Iran should do to show a genuine desire to address concerns about its nuclear program.
Zarif is a U.S.-educated diplomat appointed by Rouhani to head negotiations on the nuclear issue.
A moderate cleric, Rouhani has stepped up efforts to improve Iran's image abroad during his visit to New York this week. He has said that Iran would never develop nuclear weapons and called for a nuclear deal in three to six months. Iran says its nuclear program is for peaceful energy purposes only.
U.S. President Barack Obama on Tuesday cautiously embraced Rouhani's gestures as the basis for a possible nuclear deal and challenged him to demonstrate his sincerity.
But the failure to orchestrate a handshake between the two leaders, apparently due to Rouhani's concerns about a backlash from hardliners at home and perhaps Obama's concerns about the possibility of a failed overture, underscored how hard it will be to make diplomatic progress.
Even without making any real concessions so far, Rouhani has offered a softer, more reasonable tone than his stridently anti-U.S. predecessor, Mahmoud Ahmadinejad.
Iranians are hoping to see some tangible steps taken by the Western powers - namely relief from the painful U.S., European Union and U.N. sanctions for refusing to suspend its uranium enrichment program.
Iranian oil exports have fallen by around 60 percent in the past two years as the EU stopped purchases completely and most Asian buyers drastically cut imports. Iran is now earning around $100 million from oil sales a day as opposed to $250 million two years ago.
The six powers said in February that they want Iran to stop enrichment of uranium to 20 percent, ship out some stockpiles and shutter a facility where such enrichment work is done. In return, they offered relief from sanctions on Iran's petrochemicals and trade in gold and other precious metals.
U.S. officials say that offer remains on the table.
But signaling some of the obstacles that could hamper any new diplomacy, Iran on Thursday sharply criticized the U.N. nuclear watchdog over "baseless allegations" about its atomic activity.
It was an apparent reference to the International Atomic Energy Agency's concerns, spelled out in a series of quarterly reports, about what it calls the possible military dimensions to Iranian nuclear activities.