The UN special envoy, Kofi Annan, has told the Security Council that Syria is still witnessing unacceptable levels of violence, despite a ceasefire being in place since 12 April.
Briefing diplomats in a closed-door session, Mr Annan said he was alarmed about surges in violence in Syrian cities after visits by UN monitors.
One activist group said 38 people were killed on Tuesday, mostly in Homs.
The UN wants to increase its observers in Syria from a handful to 300.
Mr Annan said the overall situation was "entirely contrary to the will of the international community".
He said he was "particularly alarmed" by reports of government forces firing on protesters in Hama.
"If confirmed, this is totally unacceptable and reprehensible," he said.
He also called for the rapid deployment of the observer mission.
The US permanent representative to the UN, Susan Rice, told a news conference that all Security Council members wanted the observers to be deployed more quickly.
Ms Rice said that it was hoped 100 observers would be in Syria within a month.
However, Ms Rice said Syria had refused at least one observer because of his nationality, and had made clear it would not admit UN staff from any country in the "Friends of Democratic Syria" group.
Meanwhile, Chinese state media reported that two Chinese observers had arrived in Syria on Tuesday.
The BBC's Laura Trevelyan at the UN says the US and its European allies are likely to question Mr Annan on how the shaky ceasefire can be safely monitored.
The Security Council remains divided on broader policy towards Syria. The Western powers are pushing for tougher action while Damascus's allies, Russia and China, say Mr Annan's six-point peace plan, which the Syrian government has agreed to, is sufficient.
Earlier Mr Annan's spokesman, Ahmed Fawzi, said satellite imagery showed the Syrian government was failing to withdraw heavy weapons from urban centres.
He also said there were credible reports that people who met monitors were then approached and sometimes killed by security forces.
Earlier an activist in Hama told the Associated Press that dissidents had been punished for coming out to greet the visiting UN observers on Sunday, when they chanted "Long live Syria! Down with Assad!"
Syrian troops reportedly fired shells and automatic weapons in the northern Arbaeen and Mashaa al-Arbaeen districts on Monday. Some 40 people were said to have died.
Another activist, named as Samer, told the BBC there have been government attacks every day and the regime is constantly breaching the ceasefire.
"What happens is the observers visit neighbourhoods in the city, then once they leave, the shooting and shelling starts again," he said.
The government said security forces "pursued armed terrorist groups" which had been attacking and killing citizens in the area.
Syrian TV also reported a car bomb had exploded in the centre of the capital on Tuesday, injuring three people.
The Local Co-ordination Committees (LCC), an activist network, said 38 people had been killed by security forces across the country on Tuesday, including 16 in the city of Homs and 11 in the suburbs of Damascus.
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.