"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," it added.
The gathering brought together the Arab League and countries such as the United States, France and Germany.
Assad on Tuesday said he accepted the plan proposed by Annan. But this has not 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 in late February, came amid continuing fighting on the ground as 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 the 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 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 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 pass a binding decision to stop the violence.
China and Russia have already blocked such a measure, vetoing a UN resolution on February 4 condemning Syria for its crackdown on protests.
Ahead of the gathering, Assad's regime declared victory over rebels and again voiced support for 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 Sunday, among them 15 members of the security forces who died in firefights across the country, the Syrian Observatory for Human Rights said.
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 recognised the opposition Syrian National Council as the "legitimate representative" of all Syrians and the "leading interlocutor for the opposition with the international community."
SNC chief Burhan Ghalioun said this meant that "the government has now become illegitimate."
A leading Syrian rebel meanwhile hit out at the conference for avoiding the issue of arming the insurgents, saying such meetings "prolonged" the life of Assad's regime.
"We want leaders to work for an immediate end to the killings and not take decisions that extend the life of the regime," Free Syrian Army military council secretary Captain Ammar al-Wawi told AFP by telephone.
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.
Ghalioun announced however that the SNC would pay the salaries of Free Syrian Army (FSA) fighters.
"The SNC will take charge of paying fixed salaries for all officers, soldiers and resistants belonging to the FSA," he said.
Diplomats at the conference said Saudi Arabia, Qatar, and one or two other Arab countries had agreed to pay several million dollars to fund the FSA.
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 had openly called for arming the anti-Assad movement.
The United States has ruled out arming the rebels.
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 Assad's ruling party by the same name.
Annan did not attend the conference and China and Russia, Damascus's two remaining major allies, also opted out.