Syria has said it will not use chemical weapons against its own people, but would do so against an external attack.
Acknowledging their existence for the first time, Damascus said the weapons, stored and secured by the armed forces, would never be used "inside Syria".
Rebels have told the BBC's Paul Wood in Syria that they are encouraged by the killing of four top security officials.
But the refugee crisis has deepened, and Iraq has announced it is opening its borders to help people flee.
An estimated 1.5 million people are homeless within Syria, according to the Syrian Arab Red Crescent, which says the number is rising.
"Any chemical or biological weapons will never be used, I repeat, will never be used in the Syrian crisis, no matter what the internal developments in this crisis are," Mr Makdissi said, at a news conference broadcast on Syrian state TV.
"All varieties of these weapons are stored and secured by the Syrian armed forces and under its direct supervision, and will not be used unless Syria is subjected to external aggression."
Until now, Syria has never officially confirmed it has chemical weapons. It is not a signatory to the Chemical Weapons Convention (CWC), which outlaws production.
UN Secretary General Ban Ki-Moon said "it would be reprehensible if anybody in Syria is contemplating use of such weapons of mass destruction like chemical weapons".
While Damascus's acknowledgement that it has such arms adds a new dimension, it is not in itself significant, says Leonard Spector of the James Martin Center for Nonproliferation Studies in the US.
"This has been part of the military balance for decades," he has told the BBC news website.
The West and Israel have been deeply worried that Syria might use its stocks of chemical weapons, says the BBC's Jim Muir in neighbouring Lebanon.
On 16 July, the most senior Syrian politician to defect to the opposition told the BBC the government would not hesitate to use chemical weapons if it were cornered.
Nawaf al-Fares, Syria's former ambassador to Iraq, said unconfirmed reports indicated such weapons might have already been used.
However, the opposition has not reported any use of chemical weapons.
Meanwhile, Arab League foreign ministers have urged President Assad to resign rapidly, offering him safe passage. They say the opposition should form a transitional government.
Rebels from the Free Syrian Army (FSA) told our correspondent undercover with them near Damascus that the once-feared secret police is now a spent force, and the government is relying entirely on a weakened military.
They say the deaths of four men, including the defence minister and President Assad's brother-in-law, in a Damascus bombing on 18 July, were a severe blow to the government.
But parts of the capital that had fallen into rebel hands have been recaptured by government forces.
State TV on Monday showed images of troops going house-to-house and kicking down doors in Damascus, searching for rebel fighters.
Continued clashes were reported in the northern city of Aleppo.
Rebels launched a new offensive at the weekend, vowing to take the city completely and use it as a base for liberating the whole country.
Videos posted online on Monday showed jubilant rebel fighters in the Sakhour district.
State TV played down the scale of the violence, saying troops were merely hunting down "terrorists".
The most senior Turkish diplomat remaining in Syria, the consul in Aleppo, has been withdrawn for consultations.
Turkey and Lebanon have taken in thousands of refugees in camps near the Syrian border and the UN refugee agency says its staff are building a camp in Jordan as well.
Around 1,000 people are arriving in Jordan every day and the agency says the site at Za'atri should be able to cope with more than 100,000 refugees.
EU foreign policy chief Catherine Ashton has announced another 20m euros for "emergency medical care, shelter, food and water to those Syrians most affected by the ever-worsening crisis, both inside and outside the country".
The aid coincided with a decision by EU foreign ministers to tighten EU sanctions on the Syrian government.
EU member states will be required to send inspectors to board planes and ships on their territory believed to be carrying weapons or suspicious supplies to Damascus.
UK Foreign Secretary William Hague called for more support for the opposition, "including helping them prepare for Syria after Assad".
Russian airline Aeroflot is to end flights to Damascus from 6 August, citing lack of demand.
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.