Forces loyal to President Bashar al-Assad subjected the Khaldiyeh and Bayada neighbourhoods of the flashpoint central city of Homs to their fiercest bombardment since the truce came into force at dawn on Thursday, monitors said.
"The bombardment of Khaldiyeh intensified this morning with an average of three shells a minute," the head of the Syrian Observatory for Human Rights, Rami Abdel Rahman, told AFP.
He said one civilian was killed in Khaldiyeh, another was killed in shelling of the Jobar neighbourhood, and a third was shot dead by a sniper in Qsour.
Shabiha pro-regime militiamen also shot dead a civilian in the town of Aqrab, in the central province of Hama.
Three civilians died in Homs shelling on Saturday, among 14 people killed nationwide ahead of a UN Security Council vote approving the dispatch of the observer mission to monitor the truce.
Elsewhere, rebel fighters clashed with security forces in Al-Bab in the northern province of Aleppo, near the town's State Security police headquarters, the Observatory said.
Syria A police station there also came under fire, the Britain-based watchdog added.
Opposition group the Local Coordination Committees said the army shelled the village of Khirbet al-Joz in the northern province of Idlib, which is base to fighters from the rebel Free Syrian Army.
It also said armoured vehicles stormed the town of Dmeir outside Damascus, launching a campaign of arrests.
Thirty-two people have been killed since the ceasefire brokered by UN-Arab League peace envoy Kofi Annan took effect, most of them civilians, the Observatory said.
The death toll is sharply down on pre-ceasefire levels after Syria announced it was halting military operations against the rebels on Thursday.
But regime forces have so far ignored another key element of Annan's peace plan – an undertaking to withdraw tanks from towns and cities, the Observatory said.
"Since the Annan plan took effect, there has not been any change in the level of military deployment. Roadblocks and tanks remain," Abdel Rahman told AFP.
The first half-dozen observers from the advance team for the UN mission were due in Damascus later on Sunday.
Annan wants the mission's numbers to swell to more than 250 but they can only leave if the fragile truce holds, and need another UN resolution to approve their deployment.
The first group boarded a plane from New York straight after the Security Council resolution was passed.
The next 25 will come from missions around the Middle East and Africa "so we can move people quickly and they are experienced in the region," UN peacekeeping department spokesman Kieran Dwyer told AFP.
China and Russia, which raised earlier reservations over the Western-drafted text, both backed the vote, ensuring passage of the first Security Council resolution on Syria since the uprising erupted in March last year.
UN Resolution 2042 approved the sending of 30 unarmed military observers as soon as possible and called on both Syrian government and opposition forces to halt "armed violence in all its forms," officials said.
It also urged the government to "implement visibly" all its commitments under Annan's peace plan, including the withdrawal of all troops and heavy guns from cities.
Assad and the opposition must also "guarantee the safety of the advance team without prejudice to its freedom of movement and access," and the "primary responsibility" for observers' safety will rest with the Syrian government.
The resolution's passage was welcomed by Syria's opposition.
"We are ready to act to make the Annan plan a success," the Syrian National Council said in a statement signed by its leader Burhan Ghalioun.
EU foreign policy chief Catherine Ashton said the resolution "presents an unequivocal call from the international community to the Syrian regime to stop violence against its population and to address urgent humanitarian needs."
"I call on the Syrian government to take this opportunity to change course, and fully cooperate with the initial observation team," she added.
Russia and China, which had vetoed two previous Security Council resolutions on Syria, strongly supported Annan's six-point peace plan, and said they are putting increased pressure on Damascus.
The opposition has repeatedly demanded the sending of international observers, and called on Syrians to take advantage of the ceasefire to stage demonstrations.
Tens of thousands marched across Syria on Friday, although protests have yet to reach the centre of the heavily guarded capital.
More demonstrations were held on Saturday, videos posted on the Internet by activists showed.
The United Nations says more than 9,000 people have been killed since the uprising began. Monitors say the death toll has topped 10,000.