An international conference in Istanbul by "Friends of Syria" countries also urged the United Nations to act to stop the violence, but steered clear of backing opposition appeals for arms to fight the regime clampdown.
In a final declaration, the conference urged Syria mediator Kofi Annan "to determine a timeline for next steps, including a return to the UN Security Council, if the killing continues."
It added: "The regime will be judged by its deeds rather than its promises. The window of opportunity for the regime to implement its commitments to joint special envoy Annan is not open-ended."
The gathering brought together the Arab League and countries like the United States, France and Germany.
Mr Assad on Tuesday said he accepted the plan proposed by Mr Annan, but hasn't stopped the shelling of opposition strongholds.
The six-point peace plan calls for an end to violence, a daily two-hour humanitarian ceasefire and access to all areas affected by fighting, as well as an inclusive Syrian-led political process, the right to demonstrate, and the release of people detained arbitrarily.
The Istanbul gathering, which followed one in Tunis late in February, came as fighting on the ground killed more people and Damascus said it had no immediate plans to pull back its forces.
Conference host Turkey warned the world would have no choice but to recognise Syrians' right to take up arms if the UN fails to act.
"If United Nations Security Council refrains from taking on the responsibility, the international community will have no chance but to accept Syrians' right to self-defence," Prime Minister Recep Tayyip Erdogan said as he opened the conference.
US Secretary of State Hillary Clinton criticised Mr Assad's regime for launching new assaults just days after accepting the Annan plan.
"Nearly a week has gone by, and we have to conclude that the regime is adding to its long list of broken promises," she said, adding that Mr Assad was "mistaken" if he thought he could defeat the opposition against him.
Arab League head Nabil al-Arabi urged conference participants to demand that the UN Security Council make a binding decision to stop the violence.
Russia and China have already blocked such a measure, vetoing a UN resolution on February 4 condemning Syria for its crackdown on protests.
Ahead of the gathering, Mr Assad's regime declared victory over rebels and again voiced support for Mr Annan's plan, but kept up its shelling of rebel positions and said it had no plans to immediately withdraw troops.
At least 40 people were killed on Sunday, among them 15 members of the security forces who died in firefights across the country, the Syrian Observatory for Human Rights said.
Mr Assad's deadly crackdown on opponents has left more than 9,000 people dead since the uprising began in March last year, according to the UN.
The "Friends of Syria" meeting on Sunday recognised the opposition Syrian National Council as the "legitimate representative" of all Syrians and the "leading interlocutor for the opposition with the international community."
The SNC on Saturday renewed calls for arming rebels, but the final statement of the Istanbul conference did not make any reference to the pleas.
An Arab League summit in Baghdad this week rejected the option of supplying arms to either side in the conflict, though members Saudi Arabia and Qatar openly called for arming the anti-Assad movement. The US has ruled out arming the rebels.
As the Istanbul conference was under way, Syria's neighbour Iraq said Mr Assad's regime will not fall and any attempts to overthrow it by force will aggravate the crisis in the region.
"We reject any arming (of Syrian rebels) and the process to overthrow the regime, because this ... will leave a greater crisis in the region," Iraqi Prime Minister Nuri al-Maliki said in Baghdad.
Damascus blasted Sunday's meeting.
"Only the naive and those who want to see through the eyes of the Americans believe that this is a conference for the friends of the Syrian people," said Al-Baath newspaper, mouthpiece of Mr Assad's ruling party by the same name.
Mr Annan did not attend the conference and Russia and China, Damascus's two remaining major allies, have also opted out.
In Istanbul, a group of nearly 60 Syrians staged a protest outside the conference building. The group waved Mr Assad's pictures and chanted slogans in favour of the regime. The police broke up the protest with tear gas.