* Rouhani says sanctions should be lifted
* Says U.S. actions more important than words
* Iran hardliners fret Rouhani going too fast
By Marcus George and Jon Hemming
DUBAI, Oct 2 (Reuters) - Iran's parliament strongly endorsed President Hassan Rouhani's diplomatic bid to dispel mistrust at the United Nations last week during a visit which ended with an historic phone call with President Barack Obama, Iranian media said.
The backing from the assembly, controlled by political factions deeply loyal to Supreme Leader Ayatollah Ali Khamenei, is a further sign that Rouhani has the support of the Iranian establishment, though there are some rumblings from hardliners.
Khamenei, the most powerful figure in Iran, has yet to comment publicly on Rouhani's trip.
Rouhani briefed parliamentarians on his trip, including discussions on Iran's nuclear dispute with the West and regional relations, the student news agency ISNA said.
A group of 230 parliamentarians, out of the total of 290, signed a statement expressing their support of Rouhani for presenting the image of a "powerful and peace-seeking Iran which seeks talks and interaction for the settlement of regional and international issues", Fars news agency said.
While Rouhani's visit to New York boosted hopes of a diplomatic breakthrough in talks to resolve the 10-year-old dispute over Iran's nuclear programme, Israeli Prime Minister Benjamin Netanyahu dismissed it on Tuesday as a ruse concocted by a "wolf in sheep's clothing".
The United States, Israel and other countries accuse Iran of using its nuclear programme as a veil for efforts to try to develop the capability to produce weapons. Iran says the programme is for peaceful energy purposes only.
Iranian Foreign Minister Mohammad Javad Zarif said Netanyahu and "the Zionist lobby" were trying to hinder negotiations.
"We will not let Netanyahu determine the future of our talks," Zarif wrote on his Facebook page. The next round of nuclear talks between Iran and six world powers is to take place in Geneva on Oct. 15-16.
Such is the mistrust between Iran and the West that a big sticking point of negotiations over Tehran's disputed nuclear programme has been who should make the first move.
Iran has insisted the United States and the European Union should ease sanctions before it makes any concessions over enriching uranium, while Western powers have argued the reverse.
Western powers are however considering easing their long-standing demand that Iran suspend all enrichment as part of a possible deal to resolve the dispute that Rouhani says he wants to reach within months, a senior EU diplomat said.
"I believe part of the game is that if the Iranians prove that whatever they are doing is peaceful, it will, as I understand, be possible for them to conduct it," Lithuanian Foreign Minister Linas Linkevicius told Reuters.
Lithuania holds the rotating presidency of the European Union until the end of this year, giving Linkevicius a closer insight into many policy debates.
"It's conditional. It is not a done deal, but nevertheless it is a possibility to explore," he said. "Thanks to this rapprochement. How it will look, we don't know."
But both Rouhani and Obama face domestic opposition to rapprochement from those who fear their president may be too willing to grant concessions before the other side takes any concrete steps.
U.S. Republicans argue that it is the sanctions that have brought about Iran's greater apparent willingness to at least discuss compromise over some aspects of its nuclear activities and so therefore now is not the time to ease pressure on Tehran.
But Rouhani said on Wednesday a growing international consensus favoured lifting sanctions against Iran.
"During my visit to New York, many of the officials of countries made moves to have meetings with the Iranian delegations and they were saying that sanctions are ineffective and some of them even said they were unjust," the student news agency ISNA quoted Rouhani as telling a cabinet meeting.
"It appears that the international environment is such that sanctions need to be put to one side," he said, but did not say which countries wanted the sanctions to be eased.
The strongest sanctions are those of the United States and the European Union on Iran's oil, gas, banking and shipping sectors and neither Washington nor Brussels has shown any sign of easing sanctions soon, at least not before Iran acts.
In Iran's view, Rouhani has taken a big step already by talking directly to Obama and now it is the turn of the United States to show evidence of its own good will.
"In my view what American officials say is not important. What is important is that they have understood that sanctions against Iran are useless," Mehr news agency quoted Rouhani as saying.
"The problems of eight years or a decade certainly can't be solved in eight or 10 days."
OPTIMISM AND SUSPICION
Separate talks between Iran and the U.N. atomic watchdog in Vienna last week however appeared to make little real headway, though both sides described their discussions as "constructive".
One Western diplomat said he had the impression that Iran and the International Atomic Energy Agency were relatively "optimistic" after the meeting. Another envoy said the discussions had been focused and the atmosphere positive.
The Iran-IAEA meeting was a "good harbinger of better relations", said Mark Fitzpatrick of the International Institute for Strategic Studies, a London-based think tank. "There is a new mood of optimism in Vienna that finally there is a way forward," he said.
But even as Iranian conservatives fall in line behind Rouhani there were signs of unease within their ranks.
Parliamentary speaker Ali Larijani praised Rouhani's address to the U.N. General Assembly, ISNA said. But Larijani, a champion of the conservative establishment, made no specific mention of Rouhani's phone call with Obama.
The head of the powerful Revolutionary Guards said on Monday the call had been premature, a possible beginning of resistance to the relative moderate Rouhani from Iranian hardliners.