At least six people have been killed in a suburb of Damascus, the Syrian capital, reports said on Tuesday, after a renewed wave of protest marches were held following nightly Ramadan prayers.
According to the Reuters news agency, security cars with machine guns assembled on a roundabout in the Erbin suburb in the city before firing on civilians.
Residents and activists inside Syria also reported that up to eight people were killed in Hama, the city at the heart of the protests on Sunday and Monday.
Independent verification of the numbers is difficult, as the limited number of foreign reporters in the country are unable to move freely.
Footage uploaded to YouTube showed fresh protests in other Syrian, held in apparent solidarity with victims of the attacks in Hama.
In another clip protesters apparently under fire from government troops were shown running for cover.
The protests follow a severe crackdown by government forces, which have reportedly killed more than 140 people in the past few days.
President Assad has praised his troops for "foiling the enemies" of Syria. In a speech to celebrate the 66th anniversary of the Syrian army on Monday, Assad was cited by Syrian state media as saying that the military "proved its loyalty to its people, country and creed".
"Its efforts and sacrifices will be admired," he said. "These sacrifices succeeded in foiling the enemies of the country and ending sedition, preserving Syria."
The European Union announced further sanctions against Syria on Monday following the crackdown. Five more officials from Damascus are now subject to travel bans and have had their assets frozen. The list of those wanted by the EU in connection with the attack on anti-government protestors now totals 30, and includes President al-Assad.
An emergency UN Security Council meeting in New York was held behind closed doors on Monday to discuss the worsening crisis, but members reportedly disagreed about whether to adopt a Western-backed statement or negotiate for a less binding resolution.
Before the meeting US Secretary of State Hilary Clinton called on Russia and China to "reconsider their positions" and to come out against Assad.
She said: "We call on President Assad to stop the slaughter now. We call on those members of the United Nations Security Council who have opposed any Security Council action that would call on Assad to stop the killing to reconsider their positions."
Foreign Secretary William Hague has ruled out military intervention.
Hague told the Today programme on Radio 4 on Monday: "It is a very frustrating situation, the levers we have are very limited." He said military action was "not a remote possibility. Even if we were in favour of that.. there is no prospect of a legal, morally sanctioned military intervention."
Hague also indicated Britain would be pushing for greater diplomatic pressure on Damascus, saying: "We do want to see additional sanctions and have agreed a further round of sanctions in the EU which will be announced later this week.
"We will continue working on this today. I would like to see a UN security council resolution to condemn this violence."
"There are nations on the security council opposed to any resolution, so we will revisit that in the coming hours and days."
US president Barack Obama said that he was "appalled" by the violence, and has vowed to continue efforts to isolate the Syrian government.
The global protest organisation Avaaz has published details of 3,000 Syrian people who they say have 'disappeared' since anti-government protests began.