Syria's U.N. Ambassador Bashar Ja'afari also accused the U.S. government of supporting "terrorists" in Syria and waging a campaign that claims Syria could use chemical weapons in the 20-month-old civil war that has killed at least 40,000 people.
The United States says it is sending only humanitarian aid and nonlethal assistance to Syrian President Bashar al-Assad's opponents, but acknowledges some allies are arming the rebels.
Assad's government accuses Saudi Arabia, Qatar, Turkey, the United States and other Western governments of supporting and arming the rebels, an allegation the governments deny.
"We have repeatedly stated publicly and through diplomatic channels that Syria will not under any circumstances use any chemical weapons that it may have, because it is defending its people from terrorists backed by well-known states, at the forefront of which is the United States of America," Ja'afari said.
"We are genuinely worried that certain states that support terrorism and terrorists could provide the armed terrorist groups with chemical weapons, and then claim they had been used by the Syrian Government," he wrote in the letter which was dated December 8 but made public on Monday.
Damascus has accused Western powers of backing what it says is a Sunni Islamist "terrorist" campaign to topple Assad, a member of the minority Alawite sect affiliated with Shi'ite Islam.
It has said that U.S. and European concerns about Assad's forces possibly resorting to chemical weapons could serve as a pretext for preparing military intervention. Western military experts say Syria has four suspected chemical weapons sites, and it can produce chemical weapons agents including mustard gas and sarin, and possibly also VX nerve agent.
"States such as the United States of America that have used chemical and similar weapons are in no position to launch such a campaign, particularly because, in 2003, they used the pretext of Iraq having weapons of mass destruction in order to justify their invasion and occupation," Ja'afari wrote.
"Since the issue was raised, Syria has stated countless times that it will not under any circumstances use any chemical weapons that it may have against its own people," he said. "The Government of the Syrian Arab Republic warns that the terrorist groups could use those weapons against the Syrian people."
Ban expressed alarm on Sunday at the worsening violence in Syria, including the reported mass killing of Alawites and alleged firing of long-range missiles on Syrian territory, Ban's spokesman said.
He spoke to Syria's Foreign Minister Walid al-Moualem on Monday morning to voice his particular concern over reports of Syrian fighter jets bombing the Palestinian Yarmouk camp in Damascus on Sunday, killing at least 25 people.
The foreign minister told Ban that Palestinians should not offer "shelter or assistance to terrorist groups" in the Yarmouk refugee camp, state television said on Monday.
The 15-member U.N. Security Council has been incapable of taking any meaningful action in the conflict. Veto powers Russia and China refuse to condemn Assad or support sanctions.