Syrian forces have renewed their crackdown on protesters, with activists saying at least 16 people have died.
Friday protests came under fire in the central city of Homs, the capital Damascus, Deir al-Zour in the east and Aleppo and Idlib near Turkey's border.
US Secretary of State Hillary Clinton urged other countries to "get on the right side of history" by cutting ties with the Syrian regime.
Earlier, she called for wider international sanctions on Damascus.
More than 1,700 people have died and tens of thousands have reportedly been arrested since the uprising against the 41-year rule of President Bashar al-Assad's family began in March.
Syrian state television admitted there had been small demonstrations after Friday prayers, but activists said they were far bigger and more widespread.
Friday's highest reported casualties were in Douma, a suburb of Damascus, where a woman and a 16-year-old were named among those who died. Syrian state TV said two security men had been shot dead in the capital.
Activists said thousands of people had come out to protest after prayers in two mosques in Deir al-Zour. Soldiers reportedly fired live ammunition as people left the mosques, sending worshippers running for cover in alleyways.
Abdel Rahman, head of the British-based Syrian Observatory for Human Rights, said there had been a major army assault with tanks and troop carriers on Kahn Sheikhun, in north-western Idlib province, killing at least one woman.
Although Friday prayers remain a focal point for protests, during the current fasting month of Ramadan opponents of the regime are treating each day like a Friday, correspondents say, with protests after evening and early-morning prayers.
"The number of people killed and injured is increasing in Ramadan," said one protester who has been taking part in daily protests.
"We used to have 20 killed every Friday but now this number is being killed almost on a daily basis," he told the BBC.
Meanwhile, rights groups accuse the regime of targeting hospitals and arresting doctors for treating injured protesters.
"Any doctor who is discovered giving help to the injured is targeted and arrested," one Syrian doctor - who did not want to be named - told the BBC.
There are reports of troops preventing the wounded from reaching hospitals in some areas, and even of removing the bodies of dead protesters from hospitals. Activists say this is to make it harder to calculate the number of people killed in the regime's campaign to quash dissent.
International journalists face severe restrictions to reporting in Syria, and it is hard to verify reports.
'Chorus of condemnation'
The crackdown comes despite a week of international diplomacy to try to halt the violence.
Turkish Foreign Minister Ahmet Davutoglu visited President Assad this week, and on returning to Ankara described the methods used by the Syrian security forces as "unacceptable".
Mrs Clinton, meanwhile, called on countries to stop buying Syrian oil and gas
While correspondents say there is little the US can do to directly pressure a regime with which it has few ties or shared interests, it has been stepping up the pressure on the Europeans, the Russians and the Chinese, to use the leverage that they do have.
"We urge those countries still buying Syrian oil and gas, those countries still sending Assad weapons, those countries whose political and economic support give him comfort in his brutality, to get on the right side of history," said Mrs Clinton on Friday.
On Thursday, she had called for wider international sanctions on Syria in an interview with CBS News,.
When asked why Washington had not called yet outright for Mr Assad to stand down, Mrs Clinton said the US was focusing on "building the chorus of international condemnation".
Earlier this week, Syria allowed international media to film the army withdrawing from the severely attacked city of Hama, a move correspondents said was clearly been aimed at appeasing Damascus's neighbour, Turkey, and other outside powers.
Syria's recent large-scale military operations have drawn international condemnation, with Saudi Arabia, Bahrain and Kuwait recalling their ambassadors from Damascus.
Mr Assad has reiterated promises of political reform, while remaining adamant his government would continue to pursue the "terrorist groups" he has blamed for the unrest.
His opponents say the regime's failure to propose any serious reforms has merely entrenched the feeling of protesters.
Sheikh Muhammad al-Yakoubi - a Syrian Sunni cleric who fled Damascus when he was removed from his position at the al-Hassan mosque for criticising the ruling regime - said the majority of Syrians now wanted Mr Assad to step down.
"The only solution now is a change of regime through a peaceful transition of power to a new democratic Syria," he told BBC World TV from Birmingham.
"We are looking for the international community to exert some kind of pressure on the regime to let people demonstrate."