Top diplomats from 17 countries, as well as the United Nations and the European Union, gathered in Vienna for talks bringing together all the main outside players in the four-year-old Syrian crisis for the first time.
The meeting came as US officials said that the United States will deploy "fewer than 50" special operations forces to northern Syria in an advisory role.
The West and Gulf monarchies led by Saudi Arabia want Assad to step down, but Moscow and Tehran insist he has a right to play a role in an eventual transition towards a mooted unity government and later elections.
Russian President Vladimir Putin's spokesperson Dmitry Peskov said Friday's talks were not about whether Assad should go.
"It is not the fate of Bashar al-Assad that is being discussed," he told reporters in Russia.
"Any political settlement is hard to achieve before the forces of terrorism and extremism sustain a significant blow."
Iran's deputy foreign minister Hossein Amir-Abdollahian also strongly denied reports that Tehran was ready to accept a scenario under which Assad would step down within six months, Iranian state television reported.
Vienna meet could lead to wider Saudi-Iran talks: UN
But Iran nevertheless joined the talks for the first time, in a sign of its growing diplomatic clout months after striking a landmark nuclear deal with world powers.
There were some signs of progress in Vienna, with Russia and Saudi Arabia exchanging a list of Syrian opposition groups with which they have contact, Russian deputy foreign minister Mikhail Bogdanov said, quoted by RIA Novosti state news agency.
US Secretary of State John Kerry sat at the head of the table for the meeting, which also included senior envoys from Turkey, Italy, Britain, Lebanon, Jordan, Russia, Iraq, Egypt, Germany, Qatar, France, the UAE, Oman and China.
Mideast foes join key talks on Syria's fate
The Syrian regime and the opposition were not represented at the discussions aimed at ending a war that has claimed a quarter of a million lives.
Saudi Foreign Minister Adel al-Jubeir -- whose kingdom supports anti-regime rebels -- was sat almost as far from his Iranian counterpart Mohammad Javad Zarif as was possible at the tight U-shaped table in a conference room of Vienna's Imperial Hotel.
Just ahead of the talks, 40 people were killed Friday when rockets fired by Syrian government forces crashed into a market in a rebel-held area outside Damascus, the Syrian Observatory for Human Rights said.
Kerry, while warning against expectations of an immediate solution, said he was hopeful about the talks.
"I don't call it optimism. I am hopeful that we can find a way forward. It is very difficult," he said ahead of the main meeting.
Russia, which has waged a month of intense air strikes against Assad's armed opponents, has urged preparations for parliamentary and presidential elections in Syria.
But the idea has been rejected by rebels who say a vote would be impossible in the current circumstances, with millions of Syrians displaced, cities standing in ruins and two-thirds of the country in the hands of extremists and other armed groups.
Iran foreign minister will join Syria talks in Vienna
Mounting international concerns about the outpouring of Syrian refugees and the growing extremist threat could set the scene for some kind of political compromise, experts say.
"Overall, we have for the very first time around the table all the major actors and we have a situation of fatigue on the ground, so it could lead to a potential breakthrough," said Karim Bitar, of the Paris-based Institute for International and Strategic Relations.
Underscoring the perils facing those fleeing the war, 26 migrants, including at least 17 children, drowned during the night making the perilous journey from Turkey to Greece as they made a desperate bid to reach Europe.
Their nationalities were not immediately clear but the route is favoured by Syrian refugees and becoming increasingly dangerous as winter approaches.
Even getting Iran and Saudi Arabia -- the Middle East's foremost Shia and Sunni powers which back opposing sides in conflicts across the Arab world -- to sit at the same table was seen as progress.
Jubeir, in an interview with the BBC, made it clear that Riyadh is sticking by its view that Assad must leave office quickly.
"He will go either through a political process or he will be removed by force," he warned.
The West has accused Russia of concentrating its air campaign in Syria on moderate opposition groups opposed to Assad's rule, although Moscow says it is focusing on defeating the Islamic State group and other "terrorist" organisations.
Iran and Lebanon's Shia armed movement Hezbollah have troops in Syria to advise or support Assad's forces.
The Pentagon has announced plans to step up its year-old air strikes on IS extremists in Syria and Iraq, including even possible "direct action on the ground".
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