Foreign Minister Bob Carr is calling on Russia to back the formation of transitional government to stop the bloodshed in Syria.
World leaders, including delegates from the United States, Russia and the Arab League, agreed to plan for a transition at a meeting in Geneva.
The plan would see the formation of a transitional government, which could include current members of the government and opposition.
There was no explicit call for Mr Assad to cede power, though Senator Carr says a new regime is unlikely to include president Bashar Al-Assad.
But Mr Assad continues to have Russia’s support, with Moscow arguing that no-one should be excluded from any future government.
Senator Carr says Russia plays a crucial role in moving towards peace.
“At the Friends of Syria meeting to be held in Paris this Friday, I’ll be stressing that we won’t have a peaceful transition in Syria in practical terms without support from the Russians,” he said.
“This is an opportunity for Russia to show its world leadership, to show that it is responding to the deep humanitarian concerns about what is happening in Syria.
“The world is moving, there is talk about a transition plan.”
Senator Carr’s calls come after US secretary of state Hillary Clinton and UN special envoy Kofi Annan both expressed doubt that Mr Assad could play any role in a future Syrian government.
And in a clear reference Mr Assad, Mr Annan said he doubts Syrians would choose anyone with blood on their hands.
Speaking after the summit, Mr Annan called the level of violence in Syria gravely alarming.
He says there must be a fresh commitment to a ceasefire on all sides, and both the government and opposition must work together.
“We have offered a perspective for the future that can be shared by all in Syria: a genuinely democratic and pluralistic state with free and fair elections, full respect for human rights and the rule of law,” he said.
“There must be a commitment to accountability and national reconciliation.”
Meanwhile, fighting in Syria has only intensified in recent weeks as both government and opposition forces have received more weapons from their foreign backers.
The Syrian Observatory for Human Rights warned of a “catastrophic humanitarian situation” in besieged Douma, which “has been subjected to a fierce military campaign since June 21.”
Violence has killed “scores and wounded hundreds” there since regime forces escalated attacks on the outlying suburb of Damascus, the group said.
“More than 100 families remain in the town, unable to flee and forced to take refuge in shelters,” it said.
An explosion also rocked the Qaboon district of Damascus on Saturday and another blast hit the country’s second city Aleppo in the north. A further blast hit an oil pipeline in a rebel-held area of the eastern province of Deir Ezzor.
The latest violence came a day after 73 people were killed nationwide, among them 23 regime troops.
It is believed about 700 people have been killed in Syria in the past week alone, with the Opposition putting the death toll since the uprising began at 16,000.