President Barack Obama has warned Syria's President Bashar al-Assad that his government will be held accountable if it uses chemical weapons.
He was speaking after Damascus said they would not be deployed inside Syria but would be against foreign attack.
UN Secretary General Ban Ki-moon said that any thought of using chemical weapons would be "reprehensible".
Fierce fighting has taken place in Aleppo, where rebels claim to have captured parts of the city.
There are also unconfirmed reports from activists in Homs that security forces are threatening to storm the city's central prison.
The sharp international response came hours after Syrian foreign ministry spokesman Jihad Makdissi gave Damascus's first implicit acknowledgement that a chemical weapons stockpile existed.
The weapons were safely stored, he said, and Syria would never use them against its civilians but only "in case of external aggression". In an attempt to retain some doubt about his country's unconventional weapons arsenal he later tweeted "if they exist".
The US and Israel have expressed concern about the fate of Syria's arms, with Israeli PM Benyamin Netanyahu speaking of a "great threat" of weapons sites falling into the hands of Lebanon's Shia Islamist group Hezbollah, allied to President Assad.
The State Department in Washington said any possible use of such weapons would be "completely unacceptable".
"They will be held accountable by the international community and the US, should they make the tragic mistake of using those weapons," President Obama added.
The BBC's Kim Ghattas in Washington says US officials have refused to discuss details of any contingency planning surrounding Syria's chemical weapons but they have acknowledged that US Secretary of State Hillary Clinton discussed the issue on a visit to Israel last week.
Syrian rebels said they had taken control of the Salah el-Din area of the country's most populous city, Aleppo, on Monday but fighting was continuing there and in other districts late into the evening.
A child was killed when rockets were fired at a market in the al-Bab area of the city, opposition activists said.
Unverified video showed jubilant rebel fighters capturing a tank in the Sakhour district and the BBC's Ian Pannell, on the outskirts of Aleppo, said he had seen hundreds of rebels moving towards the city.
In the capital, it was a different story as footage showed Syrian troops going from house to house searching for rebel fighters in areas of Damascus that had been recaptured from the opposition.
Civilians in the Qabun area of the city complained of not being able to leave their homes and government forces were said to have taken up positions in Midan, held earlier by rebels.
Explosions and fires have been reported from the jail in the central city of Homs, where unarmed policemen are said to have defected and prisoners have staged a sit-in. Government officials had earlier denied there had been a defection.
Meanwhile, the refugee crisis is escalating both inside and outside Syria.
An estimated 1.5 million people are homeless within the country, according to the Syrian Arab Red Crescent. Another 115,000 Syrians have fled to neighbouring countries.
- 42,600 refugees are in camps in Turkey
- 34,700 refugees are in Jordan where a refugee camp for 110,000 is being set up by the UN
- 29,900 refugees are in Lebanon
- 7,500 refugees are in Iraq, where PM Nuri al-Maliki has announced that the borders should be opened for people fleeing from Syria
- EU foreign policy chief Catherine Ashton has announced another 20m euros for medical care, shelter, food and water
- Cypriot and EU officials have drafted plans for a large-scale evacuation of EU nationals from Syria as a "worst-case scenario"
On Sunday, the Syrian Observatory for Human Rights reported that at least 19,106 people had been killed since March 2011. The UN said in May that at least 10,000 people had been killed.
Syria blames the violence on foreign-backed "armed terrorist gangs".
In June, the Syrian government reported that 6,947 Syrians had died, including at least 3,211 civilians and 2,566 security forces personnel.