UN envoy Kofi Annan has warned that a failure to agree at talks in Geneva today on his peace plan for Syria could spark an international crisis.
Mr Annan told the meeting history would judge harshly if there was no deal on ending the bloodshed in Syria.
Russia, which sees Syria as a close ally, is said to be resisting proposals that could exclude President Assad from a transitional unity government.
Some 15,800 people have died in the 16-month uprising, rights groups say.
Before the talks started, Russia said there was a "very good chance" of finding common ground, but a US official said areas of "difficulty and difference" remained.
Violence has continued in Syria, despite a nominal ceasefire brokered by Mr Annan as part of his six-point peace plan.
More than 180 people were killed on Friday, rights groups said, after Syrian forces shelled a suburb of the capital Damascus and the restive central city of Homs.
One Syrian human rights group said about 4,700 of the 15,800 killed since the uprising began had died since mid-April, when the ceasefire was supposed to enter into force.
Mr Annan warned participants at the Geneva conference that they would be responsible for any further loss of life inside Syria, as well the threat posed by a continuing conflict to the wider region and the world.
"History is a sombre judge and it will judge us all harshly if we prove incapable of taking the right path today," he said.
British Foreign Secretary William Hague said the conference's decisions should be endorsed by a UN Security Council resolution permitting action to enforce the peace plan, according to the Reuters news agency, but noted that Russia was opposed to this.
He also reiterated that President Assad and his close allies should not be allowed to take part in the interim Syrian administration being discussed at the talks.
Russia has been hostile to any solution that would see Mr Assad forced out.
Meanwhile, Mr Assad said he would not accept any solution to his country's crisis imposed from outside.
He told Iranian television that it was an "internal issue" which had "nothing to do with foreign countries", stressing that no amount of foreign pressure would make his government change its policy on internal security.
Western powers, Russia, Turkey and Arab countries, including Qatar, are taking part in the Geneva meeting.
Saturday's conference in Geneva was called by Mr Annan after the violence intensified in Syria.
Russian Foreign Minister Sergei Lavrov and US Secretary of State Hillary Clinton met in St Petersburg on Friday in an effort to agree a consensus formula to end the bloodshed.
After leaving the talks with Mrs Clinton, Mr Lavrov said: "We have a very good chance to find common ground at the conference in Geneva tomorrow [Saturday].
But a US state department official later told reporters: "There are still areas of difficulty and difference."
Mr Annan wants support for an interim government that could include opposition members and officials serving under Mr Assad, but exclude those "whose continued presence and participation would undermine the credibility of the transition and jeopardise stability and reconciliation", his spokesman said.
Diplomats said this was an implicit reference to the Syrian president.