Assad also said his government will start submitting data on its chemical weapons stockpile a month after signing the convention banning such weapons.
Syria's U.N. ambassador Bashar Ja'afari told reporters Thursday that he presented Secretary-General Ban Ki-moon with "the instrument of accession" to the Chemical Weapons Convention making his country a full member of the treaty banning the use of chemical weapons.
The treaty states that a nation becomes a party 30 days after such a letter is submitted.
U.N. associate spokesman Farhan Haq said the secretary-general welcomes the development.
"Given recent events, he hopes that the current talks in Geneva will lead to speedy agreement on a way forward which will be endorsed and assisted by the international community," Haq said.
But American officials, meeting with their Russian counterparts in Geneva, insisted on a speedier Syrian accounting of their stockpiles.
Assad's remarks to Russia's state Rossiya 24 news channel were his first since the Russian plan was announced Monday as a way to avert a potential U.S. military strike in response to the Aug. 21 chemical weapons attack that killed hundreds near Damascus.
He said that Syria is relinquishing control over its chemical weapons because of Russia.
"We agreed to put Syria's chemical weapons under international supervision in response to Russia's request and not because of American threats," Assad said.
"In my view, the agreement will begin to take effect a month after its signing, and Syria will begin turning over to international organizations data about its chemical weapons," Assad added. He said this is "standard procedure" and that Syria will stick to it.
"There is nothing standard about this process," U.S. Secretary of State John Kerry retorted in Geneva, because Assad has used his chemical weapons. "The words of the Syrian regime in our judgment are simply not enough."
Syria had long rejected joining the Chemical Weapons Convention, which requires all parties to the treaty to declare and destroy whatever chemical weapons they may possess.
Assad said the Russian deal was a two-sided process. "We are counting, first of all, on the United States stop conducting the policy of threats regarding Syria," he said.
Syria's Deputy Prime Minister Qadri Jamil also suggested on Thursday that the Russian proposal will succeed only if the United States and its allies pledge not to attack Syria in the future.
"We want a pledge that neither it (the U.S.) nor anyone else will launch an aggression against Syria," Jamil told The Associated Press in Damascus.
But Kerry cautioned that a U.S. military strike could occur if Assad doesn't agree to dismantle his chemical arsenal properly. "There ought to be consequences if it doesn't take place," he said.
Russian Foreign Minister Sergey Lavrov, however, said the dismantling "will make unnecessary any strike against the Syrian Arab Republic."
Syria's top rebel commander, meanwhile, slammed the Russian proposal, calling for Assad to be put on trial for allegedly ordering the Aug. 21 attack. Many rebels had held out hopes that U.S.-led punitive strikes on Assad's forces would help tip the scales in their favor in Syria's civil war, which has claimed over 100,000 lives so far.
Gen. Salim Idris' statement was broadcast on pan-Arab satellite channels hours before talks in Geneva between Kerry and Russian Foreign Minister Sergey Lavrov.
"We call upon the international community, not only to withdraw the chemical weapons that were the tool of the crime, but to hold accountable those who committed the crime in front of the International Criminal Court," Idris said.
He added that the Free Syrian Army "categorically rejects the Russian initiative" as falling short of the expectations of rebel fighters.
The U.S. accuses Assad's government of being behind the attack in the suburb of Ghouta. The U.S. says the attack killed 1,429 people; other estimates of the deaths are lower.
Assad has denied responsibility and accuses U.S. officials of spreading lies without providing evidence.
In the interview Thursday, he charged that the Aug. 21 chemical weapons attack was a "U.S.-organized provocation."
"The threats (of a military strike) are based on a provocation. It was arranged with the use of chemical weapons in the Damascus suburb of Ghouta," he said.
In Geneva, Kerry and a team of U.S. experts will have at least two days of meetings with their Russian counterparts. The Americans hope to emerge with an outline of how some 1,000 tons of chemical weapons stocks and precursor materials as well as potential delivery systems can be safely inventoried and isolated under international control in an active war zone and then destroyed.
In Washington, officials said the CIA has been delivering light machine guns and other small arms to Syrian rebels for several weeks, following President Barack Obama's decision to arm the rebels.
The agency also has arranged for the Syrian opposition to receive anti-tank weapons like rocket-propelled grenades through a third party, presumably one of the Gulf countries that has been arming the rebels, a senior U.S. intelligence official and two former intelligence officials said Thursday. They spoke on condition of anonymity because they were not authorized to discuss the classified program publicly.
Loay al-Mikdad, a Free Syrian Army spokesman, told the AP that they have not received any weapons from the U.S. although they expect some in the near future.
Meanwhile, the Syrian Observatory for Human Rights said rebels fighting Assad's forces on Thursday captured the village of Imm al-Lokas in the southern region of Quneitra near Syria's Israeli-occupied Golan Heights.
The Britain-based activist group added that rebels also captured several army posts in the area in heavy fighting that caused casualties on both sides.
It also said that in the northeastern province of Hassakeh, clashes pitting Kurdish fighters against members of the al-Qaida-linked Nusra Front and the Islamic State in Iraq and the Levant in the past two days killed 13 Kurdish gunmen and 35 militants.
The two sides have been fighting in northern Syria for months in battles that left scores of people dead on both sides.
Syrian state media said government troops advanced in the predominantly Christian village of Maaloula near Damascus, capturing the main square as well as the Mar Takla convent where several nuns were staying.
A resident in the village told the AP that troops were trying to capture a rebel-held hotel on a hill overlooking the area. The man, who spoke on condition of anonymity for fear of reprisals, said most of the fighting Thursday was taking place in the western part of the village.
Government troops are trying to flush out rebel units, including two linked to al-Qaida, from the hilltop enclave the rebels broke into last week.
Most of the village's 3,300 residents have fled to safer parts of the country, although some have remained, hunkering down in their homes, activists said.
Maaloula, about 60 kilometers (40 miles) northeast of Damascus, had until recently been firmly in the regime's grip despite being surrounded by rebel-held territory. The village was a major tourist attraction before the civil war. Some of its residents still speak a version of Aramaic, a biblical language believed to have been used by Jesus.
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