Iran's President Hassan Rouhani called Bashar al-Assad to reaffirm his support for the Syrian leader in the wake of a U.S. missile strike, Rouhani's office said on Sunday. 

Russian President Vladimir Putin has stolen the spotlight at the United Nations with a swaggering push on the Syria crisis as he tried to shake off Western isolation over Ukraine.

In his first speech to the UN General Assembly in a decade, Putin on Monday called for a broad UN-backed coalition to fight Islamic State (IS) jihadists before sitting down to talks he called "constructive, business-like and surprisingly open" with his U.S. rival Barack Obama.

Russian President Vladimir Putin and his U.S. counterpart Barack Obama met Monday on the crisis in Syria but failed to resolve their dispute over the future role of Bashar Assad.

In dueling speeches before the U.N. General Assembly, Obama branded the Syrian leader a child-killing tyrant while Putin said the world should support Assad against the Islamic State group.

More than 150,000 trained and equipped fighters in pro-government groups, including Hizbullah, have become an indispensable brace for a Syrian army beleaguered by well over four years of intractable conflict.

"There are more than 25 main militias of different sizes that fight alongside the Syrian army" and number between 150,000 and 200,000 men, a security source told Agence France Presse.

U.S. Secretary of State John Kerry said Saturday that Syrian President Bashar al-Assad must step down, but not necessarily immediately upon reaching a settlement to end the country's civil war.

Speaking after talks in London with British Foreign Secretary Philip Hammond, Kerry said he was prepared to negotiate to achieve a solution but asked whether Assad was.

U.S. Secretary of State John Kerry raised U.S. concerns about reports of "an imminent enhanced Russian military buildup" in Syria, in a phone call Saturday to his counterpart in Moscow, the U.S. State Department said.

"The secretary made clear that if such reports were accurate, these actions could further escalate the conflict, lead to greater loss of innocent life, increase refugee flows and risk confrontation with the anti-ISIL coalition operating in Syria," the State Department said.

The White House on Thursday said it was closely monitoring reports that Russia is carrying out military operations in Syria, warning such actions, if confirmed, would be "destabilizing and counter-productive." 

"We are aware of reports that Russia may have deployed military personnel and aircraft to Syria, and we are monitoring those reports quite closely," said spokesman Josh Earnest. 

Former CIA chief and retired general David Petraeus wants the United States to consider working with some members of al-Nusra Front to tackle the Islamic State group in Syria, he said Tuesday.

In a statement to CNN, Petraeus said some members of al-Nusra Front might be persuaded to join the coalition battling the IS group.

The U.S. is struggling to implement its training program for moderate Syrian rebels fighting the Islamic State group, according to figures released Thursday by the Pentagon.

Only "100 to 200" fighters have actively begun training at U.S. sites in Jordan and Turkey, according to Pentagon spokesman Colonel Steve Warren, of the 5,000 forces the military says it wants to train over the year.

A rebel alliance including al-Qaida's al-Nusra Front seized more territory in northwestern Syria overnight, strengthening its position on the borders of two key largely regime-controlled provinces, a monitor said Saturday.

The Army of Conquest rebel alliance had made a series of sweeping gains in Idlib province, said the Syrian Observatory for Human Rights, a Britain-based monitor.