It said the regime must not be allowed to use diplomacy "to indefinitely stall international action while it continues its policy of widespread violence against civilians."
Syria's acceptance of a Russian proposal to relinquish its chemical weapons stockpile has for now averted a U.S. military strike in response to the alleged chemical weapons attack that killed hundreds near Damascus on Aug. 21.
The U.S. accuses Assad's government of being responsible for the attack in the suburb of Ghouta, saying 1,429 people were killed; others estimated a lower death toll.
Assad has denied responsibility, blaming the rebels and accusing Washington of spreading lies without evidence to justify a military strike.
U.N. Secretary-General Ban Ki-moon said he believes there will be "an overwhelming report" from the world body's inspectors that chemical weapons were used in the attack, but he did not say who was responsible. Under the mandate for the inspectors, the team was to determine whether or not chemical agents were used and if so, which agent.
The chief chemical weapons inspector, Ake Sellstrom, told The Associated Press that he has completed his report and will deliver it to Ban in New York this weekend.
Ban also said the Assad's regime "has committed many crimes against humanity."
"Therefore, I'm sure that there will be surely the process of accountability when everything is over," Ban said in remarks shown on U.N. television.
Fighting in the civil war continued. Activists said government troops battled for the ancient Christian village of Maaloula, northeast of the capital of Damascus; regime warplanes bombed rebel positions in the southern province of Daraa and in the eastern oil-rich province of Deir el-Zour; and both sides clashed in Barzeh, on the edge of Damascus.
Russian President Vladimir Putin praised Syria's joining of the Chemical Weapons Convention, telling an international security meeting in Kyrgyzstan that the move proved Damascus' "serious intentions." The summit was dominated by Russia, China and Iran, all Assad allies.
Syria's opposition said it was "deeply skeptical," and rebel commanders accused Assad of moving the chemical weapons to make tracking them more difficult.
Qassem Saadeddine, a former Syrian army colonel and spokesman for the rebels' Supreme Military Council, said the Syrian leadership has spread its chemical weapons over several dozen locations.
Saadeddine also accused Syria of sending some of the weapons to Hezbollah in Lebanon and to Iraq both close to the regime. He declined to give the source of his information.
"The chemical weapons convention requires a state to act in good faith," the SNC said. "Considering the regime's actions, this is not something the Syrian people can afford to grant the regime."
France has proposed a draft resolution that demands the weapons be put under international control and dismantled. Submitted under Chapter 7 of the U.N. charter, which makes it enforceable militarily, it warns of "very serious consequences" if Syria does not comply.
Russia has rejected any resolution under Chapter 7 and proposed a weaker presidential statement a move rejected by the U.S., Britain and France.
U.S. and Russian chemical weapons experts met in Geneva to haggle over the technical details.
The SNC urged the U.S. to keep the threat of force on the table, saying a U.N. resolution must be enforceable under Chapter 7.
U.S. Secretary of State John Kerry and Russian Foreign Minister Sergey Lavrov met in Geneva with U.N.-Arab League envoy Lakhdar Brahimi to examine political developments and plot a new international conference to support the creation of a transitional government for Syria.
Also Friday, Human Rights Watch accused Syrian government forces and pro-regime militias of carrying out mass killings of at least 248 people in two predominantly Sunni Muslim towns along the Mediterranean in May.
The New York-based group said its report on the killings in Bayda and Banias on May 2 and 3 was based on accounts of witnesses who saw or heard government and pro-government forces detain and then kill their relatives. It said 167 people were killed in Bayda and 81 in Banias.
The towns are predominantly populated by Sunni Muslims, who dominate the revolt against Assad. The towns are in Syria's coastal area, the heartland of his Alawite sect, an offshoot of Shiite Islam.
"While the world's attention is on ensuring that Syria's government can no longer use chemical weapons against its population, we shouldn't forget that Syrian government forces have used conventional means to slaughter civilians," said Joe Stork, HRW's acting Middle East director. "Survivors told us devastating stories of how their unarmed relatives were mowed down in front of them by government and pro-government forces."
The crisis began in March 2011 as largely peaceful protests against Assad, but turned into a civil war after opposition supporters took up arms to fight a government crackdown on dissent. The fighting has taken on increasingly sectarian overtones, and more than 100,000 people have been killed.
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Associated Press writers Zeina Karam in Beirut and Edith M. Lederer at the United Nations contributed to this report.