Not long after leaving, Reuters cited residents as saying that at least one mortar bomb fell in the area near the Four Seasons hotel, where the U.N. officials are staying.
Syrian state media said the bombs had been fired by "terrorists," the term it uses for rebels fighting President Bashar Assad.
Syria agreed on Sunday to allow the inspectors to visit the sites of the alleged chemical attacks. But the United States and its allies say evidence has likely been destroyed by heavy government shelling of the area over the past five days.
The attack by snipers came as Russia warned the United States that military intervention in Syria would "repeat the mistakes of the past."
Moscow said the recent escalation in pressure by Washington and its allies echoed the preamble to the 2003 U.S.-led invasion of Iraq.
(Read more: US has 'little doubt' chemical arms used in Syria: Official)
White House officials said Sunday there was "very little doubt" that the Syrian government had used chemical weapons to kill hundreds of civilians on Wednesday.
President Barack Obama discussed "possible responses by the international community" with allies including Britain and France over the weekend.
British Foreign Secretary William Hague said Monday it would be possible to respond to the "outrages" in Syria without the unanimous backing of the U.N. Security Council.
But Russia criticized the tough talk. Alexander Lukashevich, spokesman for the country's foreign ministry, said: "All these things force us to remember the events of 10 years ago, when false information about weapons of mass destruction in Iraq was used as a pretext by the U.S., who went around the UN on an undertaking, the consequences of which are well-known to all. We again firmly urge to not repeat the mistakes of the past, and not to allow actions that are out of accord with international rights."
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In an interview with a Russian newspaper, Assad denied that his forces had used chemical weapons and predicted that any U.S. military intervention in his country would be unsuccessful.
"Failure awaits the United States as in all previous wars it has unleashed, starting with Vietnam and up to the present day," he told the pro-Kremlin Izvestia newspaper. "Would any state use chemical or any other weapons of mass destruction in a place where its own forces are concentrated? That would go against elementary logic."
The Obama administration does not want to act unilaterally, an official said Sunday. The official added that the president has not yet determined whether to take action, but wants to have a clear plan in place for how to proceed in the event of U.S. military intervention.
(Read more: Hundreds die in chemical attacks, Syria rebels allege)
A senior member of the administration said any decision would be based on U.S. intelligence in addition to any findings by U.N. inspectors. The investigators have a mandate to determine if chemical weapons were used, but do not have a mandate to determine who used them, the official said.
Intelligence experts are examining harrowing video footage from rebel fighters and activists showing women and children choking to death after Wednesday's alleged attack.
Three hospitals supported by Doctors Without Borders reported to the global humanitarian group that they received roughly 3,600 patients showing neurotoxic symptoms in less than three hours Wednesday — 355 of whom reportedly died, according to a statement released by the group on Saturday.
Although the group "can neither scientifically confirm the cause of these symptoms nor establish who is responsible for the attack," the reported symptoms "strongly indicate mass exposure to a neurotoxic agent," said Dr. Bart Janssens, Doctors Without Borders' director of operations, according to the statement.
(Read more: Did Obama Draw the "Red Line" on Syria Too Soon?)
Residents of the Syrian capital also fear that their water and crops may have been contaminated because of the alleged attack, Reuters reported. The area believed to have been hit contains acres of land that supply Damascus with fresh meat, dairy, and vegetables.
Reuters contributed to this report.