"On December 21, 2013, armed terrorist groups staged a major attack against one of the sites, located in central Syria... but the authorities fought back and the attack failed," said the source.
The source did not say where in central Syria the site was located.
He also said militant groups, among them al-Qaeda-linked Al-Nusra Front and the Salafist Jaysh al-Islam, attacked a second site in Damascus province.
They "tried to attack it using an armored vehicle loaded with large amounts of explosives, but troops tasked with guarding the site fought them off and detonated the (vehicle) before it made it in."
The attack, he added, killed four regulars and wounded another 28.
Russia had warned that militant groups were fighting so close to the chemical sites.
"Attempts (to attack) these sites are ongoing," said the source.
He further said information regarding location of the site were leaked by foreign countries supporting these armed groups.
“Syria holds these countries... responsible for the danger... and for the catastrophic consequences" that such "leaks" could have, said the source.
The ministry source called on the UN and the Organization for the Prohibition of Chemical Weapons (OPCW) to "make every possible effort for these irresponsible countries to stop their practices."
The OPCW has been working in Syria since October to eliminate its chemical stockpile after a UN Security Council resolution decreed the arms must be destroyed.