France says the Security Council should consider the use of force in Syria if a UN-backed peace plan fails to stop violence in the country.
"We cannot allow the [Damascus] regime to defy us," French Foreign Minister Alain Juppe said.
Violence has continued despite a plan by international envoy Kofi Annan calling on Damascus to withdraw troops and heavy weapons from cities.
Mr Juppe said 300 UN monitors should be deployed in Syria within two weeks.
If the peace plan fails, he added, "we would have to move to a new stage with a Chapter Seven resolution (which allows for action that could be backed by force) to stop this tragedy".
There are concerns that such a resolution would be vetoed by Russia and China - which have blocked previous attempts to impose UN sanctions on Syria.
The UN has sent a small advance team of observers to Syria. Last weekend the Security Council approved the deployment of another 300.
Violence was reported on Wednesday in several parts of Syria - including in towns where observers are monitoring a ceasefire agreed earlier this month. Activists say about 20 people were killed in total.
The UK-based Syrian Observatory for Human Rights said security forces had opened fire on a bus in the north-western province of Idlib, killing four.
In Hama, seven civilians including a two-year-old girl died as the government shelled parts of the town, activists said. Two observers were staying in the centre, a short distance away.
In the southern province of Deraa, clashes were reported between armed rebels and government forces in the towns of Bosra al-Sham and Tafas. The observatory said at least six people, including soldiers, died.
Activists also said several people were killed by shelling and sniper fire in the Harasta and Douma suburbs of Damascus, despite UN monitors being in the capital.
The reports cannot be independently verified owing to government restrictions on foreign media.
The Syrian government says it is fighting armed gangs, and that the terms of the ceasefire allow its forces to respond to attacks.
Mr Annan told the Security Council on Tuesday that the Syrian military had not withdrawn its forces or heavy weapons from population centres.
He said he was "particularly alarmed by reports that government troops entered Hama [on Monday] after observers departed, firing automatic weapons and killing a significant number of people".
"If confirmed, this is totally unacceptable and reprehensible," he added.
Also on Tuesday the US permanent representative to the UN, Susan Rice, told reporters 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.