Shooting has broken out during a visit to a Damascus suburb by an advance team of UN observers, activists say.
Videos posted online appear to show anti-government protesters ducking as snipers open fire in Arbeen. Crowds are shown surrounding the UN cars.
The UN team is overseeing a shaky ceasefire brokered by UN-Arab League envoy Kofi Annan.
UN chief Ban Ki-moon is to ask the Security Council to expand the observer force from 30 to 250 members.
Meanwhile, US Secretary of State Hillary Clinton said Syria was at a "crucial turning point".
Speaking in Brussels, she said President Bashar al-Assad faced tougher measures if he squandered his "last chance" by failing to implement Mr Annan's peace plan.
She said there was a need to "tighten pressure on the regime and on those who support the regime", adding: "Every country in Nato is watching the situation with concern."
A spokesman for Mr Annan confirmed that the observers had been in Arbeen on Wednesday.
Ahmad Fazwi said it would be "appalling" if it was confirmed that Syrian forces had opened fire in the area.
The team's head, Col Ahmet Himmiche, told Reuters news agency that the observers had not come under fire. He gave no further details.
One activist video from the suburb appears to show Col Himmiche telling the crowd through a loud hailer to move back and let the cars pass.
A protester is seen placing a banner on a UN car that reads: "The killer is doing his killing, the monitors are doing their monitoring and the people are doing their revolution."
The footage cannot be verified.
Activist group the Local Co-ordination Committees said that 32 people had been killed in violence across Syria on Wednesday, despite the ceasefire that began nearly a week ago.
Activists said government forces were continuing to shell areas of Homs. Several districts remain outside government control despite a major offensive that began in February.
Mr Annan's six-point peace plan calls for Syrian forces to withdraw from residential areas; the release of political prisoners; the permitting of peaceful demonstrations; greater access for the media and the start a democratic political transition.
Syria's state news agency Sana reported on Wednesday that at least six members of the security forces had been killed by a bomb blast in Idlib province. A second blast in the Aleppo region killed four soldiers, it added.
The advance UN team arrived in Syria on Sunday.
Mr Ban is preparing to brief the UN Security Council on his proposals for a larger UN observer mission, supported by planes and helicopters from the EU.
He has said that a 250-strong mission - as proposed by Mr Annan - might not be big enough.
The UN says about 9,000 people have died since pro-democracy protests began in March 2011. In February, the Syrian government put the death toll at 3,838 - 2,493 civilians and 1,345 security forces personnel.
In other developments, Turkish authorities are due to search a ship in the port of Iskenderun following claims that it is carrying arms bound for Syria.
Both the EU and Turkey have imposed an arms embargo on Syria.
Meanwhile, the wives of the German and UK ambassadors to the UN have posted a video on YouTube urging President Assad's wife, Asma, to help end the bloodshed in her country.
They ask Mrs Assad to urge her husband to stop violent repression.