Shooting was heard in Deraa overnight, where the government this week sent tanks and troops to regain control.
Meanwhile, the UN failed to agree on a statement condemning the crackdown.
A draft proposed by France, Britain, Germany and Portugal was opposed by several within the 15-member Security Council, with Russia insisting events in Syria were not a threat to international peace.
President Bashar al-Assad's government disputes the Western view that the demonstrations have been non-violent.
In a statement carried by the official news agency, it said it had sent troops to several cities on the request of citizens who were worried about "armed extremists". Opposition leaders say the protests are peaceful.
Foreign media ban A declaration signed by the Baath party officials in Deraa said they were quitting to protest against the violent crackdown, Reuters reported.
AnalysisWhile those who have resigned are not high-ranking national figures, their public resignations and statements of denunciation are significant given the monolithic status of the Baath party, which has ruled Syria since it took power in a 1963 coup.
The defections indicate the government is losing political control of those areas - losing the hearts and minds - and is resorting to sending in tanks to impose control by force.
Meanwhile, President Assad has known from the beginning that the Arab and outside worlds would not unite against him as they did against Colonel Gaddafi in Libya, so the failure of the UN Security Council to reach agreement comes as no surprise.
In any case, it would not have affected events on the ground, where the regime is struggling to stifle its more serious challenge in nearly 50 years.
On Wednesday, footage posted on the internet appeared to show Syrian tanks heading towards Deraa to reinforce troops who had moved in on Monday.
Amnesty International quoted eyewitnesses as saying army snipers were shooting at wounded residents lying in the streets and that other people were trying to save them.
But with communications apparently cut off from the city, it is hard to be sure what is happening there.
Despite the crackdown, though, protesters have designated Friday a "day of rage" throughout the country: They say there is no turning back.
'No need to investigate' On Friday, the UN Human Rights Council is due to hold an emergency session to consider a draft resolution demanding an immediate end to President Assad's efforts to crush the challenge to his rule. Continued