Kofi Annan said an international conference in Geneva had agreed there should be a “transitional government body with full executive powers”.
This could include both members of the government and opposition.
But her Russian counterpart Sergei Lavrov said there were no preconditions to the proposed transition that dictated who should or should not be in the transitional government.
Saturday’s “action group” conference was attended by both Western powers and Russia and China.
Mr Annan also called for an immediate ceasefire and adherence to the UN’s six-point peace plan.
Some 15,800 people have died in the 16-month uprising against the rule of President Assad, activists say.
More than 180 people are said to have been killed on Friday alone as government forces reportedly shelled a suburb of the capital Damascus and the restive central city of Homs.
On Saturday, activists and witnesses said many residents were fleeing the Damascus suburb of Douma, which has come under sustained assault from government forces. Mr Annan said the international community was increasing pressure to end the violence.
Mr Annan said the international community was increasing pressure to end the violence.
“We are determined to work together urgently and intensively to bring about an end to the violence and human rights abuses, and the launch of a Syrian-led political process, leading to a transition that meets the legitimate aspirations of the Syrian people, and enables them independently and democratically to determine their own future,” he said.
He warned: “The action group has pledged action, and they are sending a message of determination and hope, but today’s words must not become tomorrow’s disappointments.
“The hard work starts now. We must work together to implement what has been agreed. We cannot do this alone. I hope all in Syria will embrace what has been laid out here and work with us to stop the killing and build a better future.”
Speaking on behalf of the five permanent members of the UN Security Council – the US, UK, France, Russia and China – British Foreign Secretary William Hague said all five were committed to supporting Mr Annan’s efforts.
Russia had blocked a provision in Mr Annan’s plan that would have called for Mr Assad to step down to make way for a unity government.
Mrs Clinton told reporters after Saturday’s talks: “Assad will still have to go… given the blood on his hands.”
Mr Assad has said he will 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.