Russia President Vladimir Putin speaks at a press conference during the G20 summit in Los Cabos, Mexico, Tuesday, June 19, 2012.
International efforts to halt the violence are deadlocked because Russia and China, which wield vetoes in the U.N. Security Council, have blocked tougher action against Assad. They say the solution must come through political dialogue, an approach most of the Syrian opposition rejects.
British Prime Minister David Cameron said Putin had shifted his view of Assad during talks with Obama and other world leaders at the Group of 20 summit in Los Cabos, Mexico, and that discussions were now focused on a transition of power in Syria.
But Putin immediately seemed to contradict that notion, telling reporters at the end of the summit: "We believe that nobody has the right to decide for other nations who should be brought to power, who should be removed from power."
Russia has been the staunchest backer of Assad and his military crackdown against militants and protesters in Syria, including supplying arms to the Syrian government.
Speaking at the summit, Obama said Assad has lost all legitimacy and that it was impossible to conceive of any solution to the violence in Syria that leaves him in power. Obama conceded he had failed to make a breakthrough with the leaders of Russia or China despite intensive talks.
"I wouldn't suggest that at this point the United States and the rest of the international community are aligned with Russia and China in their positions, but I do think they recognize the grave dangers of all-out civil war," he told reporters.
He said it is important for the world community to work with the United Nations and international mediator Kofi Annan "on what a political transition would look like. ... But I don't think it would be fair to say that the Russians and the Chinese are signed on at this point."
Alarmed but apparently impotent to resolve the crisis, the outside world is deeply divided in its response to an increasingly sectarian conflict that threatens to become a proxy war for regional powers.
The United Nations estimates more than 10,000 people have been killed in 15 months of violence and unrest.
German Chancellor Angela Merkel, French President Francois Hollande, Turkish Prime Minister Tayyip Erdogan and Cameron were present with Obama for the talks with Putin.
"There remain differences over sequencing and the shape of how the transition takes place but it is welcome that President Putin has been explicit that he does not want Assad remaining in charge in Syria," Cameron told reporters.
"What we need next is an agreement on a transitional leadership which can move Syria to a democratic future that protects the rights of all its communities," Cameron added.
Russian Foreign Minister Sergei Lavrov said Cameron's statement that Putin does not want Assad to remain in power "does not correspond to reality."
The chief U.N. monitor for Syria told the Security Council that his military observers were repeatedly targeted by hostile crowds and gunfire at close range last week before his decision to suspend operations, U.N. diplomats said.
Separately, a cargo ship off the British coast carrying weapons bound for Syria has apparently turned back towards Russia, Britain's Foreign Secretary said, calling again for a halt to arms shipments to Assad.
The Curacao-flagged cargo ship Alaed, last seen off the north-west coast of Scotland this week, was believed to carrying Russian weaponry to Syria, according to an insurer that said it had withdrawn coverage for the vessel.
The Pentagon said Russia's military was preparing to send three ships to Syria but noted that Moscow's stated intention was to send supplies and personnel to its naval facility in the Mediterranean port of Tartus.
Western nations and their Sunni Muslim allies in the Gulf and Turkey seek Assad's overthrow but are wary of intervention, while Russia, China and Shi'ite Iran - Assad's strategic ally - have protected Assad from a tough international response.
SOUNDS OF EXPLOSIONS
A resident in Homs said the sound of explosions could be heard across the city, and activists also reported shelling in the Damascus suburb of Douma and fighting between soldiers and rebels in northern Aleppo province near the border with Turkey.
The violence is the latest wave of relentless bloodshed that led United Nations observers - who were sent to Syria to monitor a ceasefire deal brokered by international mediator Kofi Annan - to halt operations on Saturday.
General Robert Mood of Norway, chief U.N. monitor for Syria, told the 15-nation Security Council behind closed doors that his 300-strong unarmed observer force was targeted with gunfire or by hostile crowds at least 10 times last week, U.N. diplomats present at the meeting told Reuters on condition of anonymity.
Mood said that "indirect fire" incidents in which gunfire struck within 300-400 meters (yards) of observers occurred on a daily basis, envoys said. Last week, nine vehicles of the observer mission, known as UNSMIS, were struck or damaged, they added.
One diplomat said Mood spoke of "several hundred indirect fire incidents."
Some Western diplomats have suggested that there was little point in having UNSMIS remain in Syria when Assad's government has not only ignored Annan's peace plan but has stepped up its military assaults to seize rebel-held territory.
UNSMIS' 90-day mandate expires on July 21 and it is unclear whether the council will extend it.
Activists say at least 2,000 people have been killed in Syria since Annan's April 12 ceasefire deal, intended to be the first stage in a political plan to resolve Syria's 15-month-old crisis, was supposed to put an end to the killing.
"There are many buildings and houses completely destroyed (in Homs), and many injuries in the field hospitals which need surgery," said one resident of Syria's third biggest city, who gave his name as Nidal.
"There are many martyrs and no medicine."
Activists said violence flared across the country on June 19 and state media said rebels blew up two oil pipelines.
SANA news agency said an "armed terrorist group" attacked a oil derivatives pipeline linking Homs and Damascus in the Sultaniya area of southern Homs, causing a fire and heavy smoke that residents said was visible from the centre of the city.A crude oil pipeline in the eastern province of Deir al-Zor was also blown up. SANA quoted an oil ministry source as saying pumping was expected to resume in the next few days, adding that the same pipeline had been targeted twice in the last two weeks.