Activists said security forces were continuing to sweep through villages near the flashpoint northeastern town of Jisr al-Shughur, which troops captured on Sunday.
"Six civilians perished in the past few hours in Ariha," east of Jisr al-Shughur, an activist told reporters in Nicosia, without providing further details.
The deaths came after fresh protests erupted in the eastern town of Deir Ezzor, a rights activist said.
Protesters have described the operation in the northern mountains as a scorched-earth campaign, while Syrian soldiers who deserted to Turkey have alleged they were forced to commit atrocities there.
Forces stationed in the town shot dead a family of four in Jisr al-Shughur on Monday, London-based rights activist Rami Abdel Rahman said.
According to a toll released Tuesday by the Syrian Observatory for Human Rights, the violence has claimed the lives of 1,297 civilians and 340 security force members in Syria since the unrest erupted mid-March.
Washington meanwhile accused Iran of backing Syria's assaults on pro-democracy protesters and again urged Assad to end the violence.
"Iran is supporting the Assad regime?s vicious assaults on peaceful protesters and military actions against its own cities," Secretary of State Hillary Clinton said.
She compared its response to the Islamic republic's 2009 crackdown on its own pro-reform protests.
"President Assad needs to engage in political dialogue," White House spokesman Jay Carney said earlier.
"A transition needs to take place. If President Assad does not lead that transition then he should step aside."
Turkish Prime Minister Recep Tayyip Erdogan telephoned Syria's President Assad on Tuesday, urging him to "refrain from violence and end the unrest", Anatolia news agency reported.
Erdogan stressed "it would be useful to draw up a timetable of reforms as soon as possible and urgently implement them," the agency added.
Although the two leaders have enjoyed close personal ties in recent years, Ankara's insistent calls on Damascus to initiate reforms have so far gone unheeded.
Last week, as thousands of fleeing Syrians crossed into Turkey to seek refuge from bloodshed, Erdogan toughened his tone, accusing the Syria of perpetrating an "atrocity" against the demonstrators.
The prominent Syrian poet Adonis, in an open letter published Tuesday in a Lebanese daily, called on Assad to let Syrians decide their own future.
"It seems your destiny is to sacrifice yourself for your mistakes and to give back voice to the people and let them decide," he wrote.
The United Nations said more than 10,000 Syrians have fled into neighbouring countries to escape the crackdown.
In Lebanon alone, there were more than 5,000, UN humanitarian affairs spokeswoman Stephanie Bunker said. A Turkish official said Tuesday they had now received more than 8,500 Syrians refugees.
"There is no water, no food, children cry all the time," one woman who had fled Jisr al-Shughur over the mountains into Turkey told AFP.
"May God punish him! He even poisoned our water. What have we done to him?"
UN emergency relief coordinator Valerie Amos again appealed to Syria to let in a UN humanitarian team make a proper assessment. But Syria is refused to let UN aid experts visit stricken towns and has also blocked access to rights investigators.
At the United Nations, European powers campaigning for a draft resolution condemning the crackdown face opposition from Russia and China, both of whom wield veto powers and object to UN action against Assad.
Refugees arriving in Turkey said fighting had also broken out among Syrian troops during the northern operation Sunday, as soldiers bent on destroying the area were confronted by others trying to defend civilians.
Damascus: Syrian troops continued their crackdown in the north of the country, with more civilian deaths reported, as the United States accused Iran of backing the assault on pro-democracy protesters.
First Published: Wednesday, June 15, 2011, 09:51