* Obama calls for strong resolution on weapons
* Russia says is "common understanding" with U.S.
* France, Turkey, Jordan urge redoubled diplomatic efforts
* Rouhani warns against threats of military action
By Steve Holland and Asma Alsharif
UNITED NATIONS, Sept 24 (Reuters) - U.S. President Barack Obama appealed to the United Nations on Tuesday to back tough consequences for Syria if it refuses to give up chemical weapons and urged Russia and Iran to end their support for Syrian President Bashar al-Assad.
Russia, Assad's main backer, said there was a "common understanding" with the United States on how to move toward agreement for a U.N. resolution that would support the chemical arms deal, but both nations said there was more work to be done.
At the same time, Obama said agreement on Syria's chemical weapons should energize a larger diplomatic effort to end 2-1/2 years of civil war - a sentiment that was echoed by the leaders of Turkey, Jordan and France, among others.
"I do not believe that military action - by those within Syria, or by external powers - can achieve a lasting peace," Obama told world leaders at the U.N. General Assembly.
Obama stepped back from launching unilateral military action against Syria this month, setting in motion a diplomatic effort that led to Russian assistance in persuading Syria to agree to give up its chemical weapons after a poison gas attack on Aug. 21 that U.S. officials say killed more than 1,400 people.
In a bid to ensure Syria fulfills its promise, Obama's challenge at the United Nations was to persuade world leaders to apply pressure on Damascus with a U.N. Security Council resolution that includes tough consequences should Assad not surrender his chemical weapons stockpiles in a verifiable way.
"The Syrian government took a first step by giving an accounting of its stockpiles. Now, there must be a strong Security Council resolution to verify that the Assad regime is keeping its commitments, and there must be consequences if they fail to do so," Obama said.
The worry from the U.S. side is that Russia might veto any resolution that contains even an implicit threat of military force against Syria. U.S. Secretary of State John Kerry met his Russian counterpart, Sergei Lavrov, on Tuesday in an effort to agree on the wording of a resolution this week.
Negotiations on a draft in New York have come to a standstill while Russia and the United States struggle to reach an agreement that would be acceptable to both, diplomats say.
"We had a very constructive meeting," Kerry told reporters after meeting with Lavrov at the United Nations for about 90 minutes. "Very constructive."
A senior U.S. official said the U.N. envoys for the two countries would now need to do more work on the draft resolution.
"We have a common understanding of how to move forward in the next few days," Lavrov told Russian reporters after the meeting in remarks posted on his ministry's website on Wednesday.
He gave no details except to say that the resolution should be based on the agreement he and Kerry reached in Geneva this month for Syria to abandon its chemical arsenal.
Western states have called for a resolution that is forceful enough to help ensure Assad complies, but Russia says that threats could have the opposite effect and that the draft should do no more than support the chemical weapons plan.
Speaking earlier in Moscow, Deputy Foreign Minister Sergei Ryabkov said Russia would not accept a resolution stipulating automatic punitive measures if Assad failed to comply with the U.S.-Russian deal.
But Western powers have apparently given up on what U.N. diplomats call a "trigger" clause for automatic punitive measures in the event of non-compliance, increasing the prospects for agreement on a draft.
Ryabkov said that while the resolution must not be adopted under Chapter 7 of the U.N. charter, which can authorise the use of force or other measures, it could potentially refer to Chapter 7 measures as a possible means to punish violations.
French President Francois Hollande told the Assembly that too much time had been wasted trying to end the civil war, which the United Nations says has killed more than 100,000 people.
"We must ensure that this war ends. It is the deadliest war since the beginning of this century. The solution is a political one and too much time has been lost," he said.
Obama said it was not for America to determine who would lead Syria, but he added: "A leader who slaughtered his citizens and gassed children to death cannot regain the legitimacy to lead a badly fractured country."
Obama had an explicit message for Assad's two biggest backers, Iran and Russia: The notion that Syria can return to a pre-war status quo "is a fantasy."
"It's time for Russia and Iran to realize that insisting on Assad's rule will lead directly to the outcome they fear - an increasingly violent space for extremists to operate," he said.
Iranian President Hassan Rouhani said there was no military solution to the Syrian crisis and criticized "some regional and international actors" for helping militarize the situation by providing arms and intelligence to "extremist groups."
In his speech to the General Assembly, Rouhani welcomed Syria's acceptance of the Chemical Weapons Convention and, in an apparent reference to U.S. threats of military action, he added: "I should underline that (an) illegitimate and ineffective threat to use or the actual use of force will only lead to further exacerbation of violence and crisis in the region."
Sheikh Tamim bin Hamad al-Thani, the emir of Qatar, which has been backing Syrian rebels, condemned what he called "horrible massacres" by the Syrian government.
"It is unfortunate that the perpetrators of these brutal crimes and massacres that have shocked every human conscience are enjoying impunity from deterrence or accountability," he told the Assembly.
In his opening speech to the General Assembly, U.N. Secretary-General Ban Ki-moon appealed to member states not to abandon the Syrian people, and said it was not enough to destroy Syria's chemical weapons while the wider war continued.
"Military victory is an illusion. The only answer is a political settlement," Ban said.
Turkish President Abdullah Gul and Jordan's King Abdullah were among the world leaders at the General Assembly who called for a more robust international effort to end Syria's civil war.
"This conflict has evolved into a real threat to regional peace and security," said Gul, whose country was once an ally of Assad but is now one of his fiercest critics. "Any recurrence of the proxy wars of the Cold War era will plunge Syria into further chaos."
King Abdullah said the number of Syrian refugees in Jordan could rise to 1 million by next year, equivalent to 20 percent of its population, and called for additional international support as the economic burdens weigh on the state.
"My people cannot be asked to shoulder the burden of what is a regional and global challenge," he said. "More support is urgently needed to send a strong signal that the world community stands shoulder-to-shoulder with those who have borne so much."
Lebanese President Michel Sleiman also warned about the repercussions on his country's security and economy from the Syrian crisis. He said the number of Syrian refugees in the country was "way beyond Lebanon's capacity of assimilation, exceeding one fourth of Lebanon's population."
Obama announced the United States would provide an additional $339 million in humanitarian aid to ease the Syrian refugee crisis, including $161 million for people inside Syria and the rest for surrounding countries.