Violence in Syria has already spilled over the past year to Lebanon, Turkey, Iraq and the Israeli-occupied Golan Heights. Battle-hardened Hezbollah fighters have joined the combat alongside Assad's forces.
Meanwhile, U.S. naval units are moving closer to Syria as President Barack Obama considers a military response to the alleged use of chemical weapons by Assad's government.
U.S. defense officials told The Associated Press that the Navy had sent a fourth warship armed with ballistic missiles into the eastern Mediterranean Sea but without immediate orders for any missile launch into Syria. The officials spoke on condition of anonymity because they weren't authorized to discuss ship movements publicly.
Obama emphasized that a quick intervention in the Syrian civil war was problematic, given the international considerations that should precede a military strike.
After Obama met with his national security team Saturday, the White House said U.S. intelligence officials are still trying to determine whether Assad's government unleashed the chemical weapons attack earlier this week.
The White House statement said Obama received a detailed review of the range of options he has requested for the U.S. and the international community to respond if it is determined that Assad has engaged in deadly chemical warfare.
Obama spoke by telephone with British Prime Minister David Cameron about Syria, the White House said.
A statement from Cameron's office at No. 10 Downing St. said the prime minister and Obama are concerned by "increasing signs" that "a significant chemical weapons attack" was carried out by the Syrian government against its people. Obama and Cameron "reiterated that significant use of chemical weapons would merit a serious response from the international community," according to the statement.
Syria's Information Minister Omran al-Zoubi dismissed the possibility of an American attack, warning that such a move would risk triggering more violence in the region.
"The basic repercussion would be a ball of fire that would burn not only Syria but the whole Middle East," al-Zoubi said in an interview with Lebanon-based Al-Mayadeen TV. "An attack on Syria would be no easy trip."
In Tehran, Iran's Foreign Ministry Spokesman, Abbas Arakji, warned that an American military intervention in Syria will "complicate matters."
"Sending warships will not solve the problems but will worsen the situation," Arakji said in comments carried by Iran's Arabic-language TV Al-Alam. He added that any such U.S. move does not have international backing and that Iran "rejects military solutions."
In France, Doctors Without Borders said three hospitals it supports in the eastern Damascus region reported receiving roughly 3,600 patients with "neurotoxic symptoms" over less than three hours on Wednesday morning, when the attack in the eastern Ghouta area took place.
Of those, 355 died, the Paris-based group said.
The Britain-based Syrian Observatory for Human Rights said Saturday that its estimated death toll from the alleged chemical attack had reached 322, including 54 children, 82 women and dozens of fighters. It said the dead included 16 people who have not been identified.
The group said it raised its death toll from an earlier figure of 136, which had been calculated before its activists in the stricken areas met doctors, residents and saw medical reports. It said the dead "fell in the massacre committed by the Syrian regime."
Death tolls have varied wildly over the alleged attack, with Syrian anti-government activists reporting between 322 and 1,300 killed.
Al-Zoubi blamed the rebels for the chemical attacks in Ghouta, saying that the Syrian government had proof of their responsibility but without giving details. "The rockets were fired from their positions and fell on civilians. They are responsible," he said.
With the pressure increasing, Syria's state media accused rebels in the contested district of Jobar near Damascus of using chemical weapons against government troops Saturday.
State TV broadcast images of plastic jugs, gas masks, vials of an unspecified medication, explosives and other items that it said were seized from rebel hideouts Saturday.
One barrel had "made in Saudi Arabia" stamped on it. The TV report also showed medicines said to be produced by a Qatari-German medical supplies company. Qatar and Saudi Arabia are strong supporters of the Syrian rebels. The report could not be immediately verified.
An army statement issued late Saturday said the discovery of the weapons "is clear evidence that these gangs are using chemical weapons against our people and soldiers with help from foreign sides."
The claims could muddy the debate about who was responsible for Wednesday's alleged gas attack, which spurred demands for an independent investigation and renewed talk of potential international military action if chemical weapons were used.
Just hours before the state media reports, the U.N. disarmament chief arrived in Damascus to press Assad's regime to allow U.N. experts to investigate the alleged Wednesday attack. The regime has denied allegations it was responsible, calling them "absolutely baseless" and suggesting they are an attempt to discredit the government.
The U.S., Britain, France and Russia have urged the Assad regime and the rebels fighting to overthrow him to cooperate with the United Nations and allow a team of experts already in Syria to look into the latest purported use of chemical agents. The U.N. secretary-general dispatched Angela Kane, the high representative for disarmament affairs, to push for a speedy investigation into Wednesday's purported attack. She did not speak to reporters upon her arrival in Damascus Saturday.
The state news agency said several government troops who took part in the Jobar offensive experienced severe trouble breathing or even "suffocation" after "armed terrorist groups used chemical weapons." It was not clear what was meant by "suffocation," and the report mentioned no fatalities among the troops.
"The Syrian Army achieved major progress in the past days and for that reason, the terrorist groups used chemical weapons as their last card," state TV said. The government refers to rebels fighting to topple Assad as "terrorists."
State TV also broadcast images of a Syrian army officer, wearing a surgical mask, telling reporters wearing similar masks that soldiers were subjected to poisonous attack in Jobar. He spoke inside the depot where the alleged confiscated products were placed.
"Our troops did not suffer body wounds," the officer said. "I believe terrorist groups used special substances that are poisonous in an attempt to affect this advance."
Al-Mayadeen aired interviews with two soldiers hospitalized for possible chemical weapons attack. The two appeared unharmed but were undergoing tests.
"We were advancing and heard an explosion that was not very strong," a soldier said from his bed. "Then there was a strange smell, my eyes and head ached and I struggled to breathe." The other soldier also said he experienced trouble breathing after the explosion.
Al-Mayadeen TV, which has a reporter embedded with the troops in the area, said some 50 soldiers were rushed to Damascus hospitals for treatment and that it was not yet known what type of gas the troops were subjected too.
In Turkey, top Syrian rebel commander Salim Idris told reporters that opposition forces did not use chemical weapons on Saturday and that "the regime is lying."
For days, the government has been trying to counter rebel allegations that the regime used chemical weapons on civilians in rebel-held areas of eastern Damascus, arguing that opposition fighters themselves were responsible for that attack.
French Foreign Minister Laurent Fabius dismissed the Syrian government's claims.
"All the information we have is converging to indicate there was a chemical massacre in Syria, near Damascus, and that Bashar Assad's regime was behind it," Fabius told reporters during a visit to the West Bank city of Ramallah. He did not elaborate.
France has suggested that force could be used against Syria if Assad's regime was proven to have used chemical arms.
The new talk of potential military action in in the country has made an independent investigation by U.N. inspectors critical to determine what exactly transpired.
The U.N. experts already in Syria are tasked with investigating three earlier purported chemical attacks in the country: one in the village of Khan al-Assal outside the northern city of Aleppo in March, as well as two other locations that have been kept secret for security reasons.
It took months of negotiations between the U.N. and Damascus before an agreement was struck to allow the 20-member team into Syria to investigate. Its mandate is limited to those three sites, however, and it is only charged with determining whether chemical weapons were used, not who used them.
Leaders of the main Western-backed Syrian opposition group on Saturday vowed retaliation for the alleged chemical weapons attack.
From Istanbul, the head of the Syrian National Coalition, Ahmad Al-Jarba, also criticized the lack of response to the attack by the United Nations and the international community, saying the UN was discrediting itself.
"It does not reach the ethical and legal response that Syrians expect," he said. "As a matter of fact we can describe it as a shame."
Mroue reported from Beirut. Associated Press writers Jamey Keaten in Paris, Desmond Butler in Istanbul and Bradley Klapper in Washington contributed to this report.