Syrian security forces killed six demonstrators as more than half a million people took to the streets across the country on Friday to demand the departure of Bashar al-Assad, activists said.

The protests came as US Secretary of State Hillary Clinton said time was running out for the Syrian president, as he pursues a violent crackdown on pro-democracy activists that has killed more than 1,300 since mid-March.

At least three people died in the central city of Homs when security forces opened fire to quash protests, two were killed in Damascus and one in Daraya, near the capital, activist Ammar Qorabi told AFP in Nicosia.

Earlier, an activist in Homs, 160 kilometres (100 miles) north of Damascus, had said two died and at least 12 were wounded, with tanks in the city, and that "more than 100,000 people participated today in demonstrations in several districts."

In Hama, 40 kilometres further north, varying reports put the turnout at as much as more than half a million.

The head of the Syrian Observatory for Human Rights, Rami Abdel Rahman, gave a figure of more than 500,000 and said this was "the biggest (anti-regime) demonstration since the Syrian Revolution broke out" on March 15.

Another activist said that "more than 400,000 marched," adding that "they came from all over, from mosques and nearby towns."

A third said earlier that more than 200,000 had gathered in the city's Assi Square, stretching for more than one kilometre, and that there was no sign of security forces.

Abdel Karim Rihawi, president of the Syrian League for Human Rights, said "tens of thousands of protesters headed towards Deir Ezzor's Freedom Square upon leaving the mosques" after the main weekly Muslim prayers in the eastern oil hub on the Euphrates River.

In Jabal al-Zawiyah, which has been the theatre of army operations since Tuesday, "tens of thousands of people started to march from the village towards Maaret al-Numan," he told AFP.

For its part, state television showed images of pro-regime demonstrations in the country's commercial hub of Aleppo, in the north, and in Suweida, in the south.

People were waving Syrian flags and chanting "God, Syria, Bashar and that's it."

Overnight, Abdel Rahman said security forces had killed three civilians in Jabal al-Zawiyah, as explosions were heard in the coastal city of Latakia.

Before Friday's protests, US Secretary of State Hillary Clinton criticised the Assad regime's incoherence in authorising an opposition meeting while stifling dissent.

"Allowing one meeting of the opposition in Damascus is not sufficient," she told reporters on a visit to Lithuania.

"I'm just hurt by recent reports of continuing violence on the border and in Aleppo, where demonstrators have been beaten, attacked with knives by government-organised groups and security forces," Clinton said.

"It is absolutely clear that the Syrian government is running out of time. There isn't any question about that."

Friday's protests followed a call from a Facebook group for people to take to the streets nationwide.

The Syrian Revolution 2011 group called on people to rally after weekly prayers, branding July 1 "the Friday of departure" and saying in a message to Assad: "We don't love you... Go away, you and your party."

Hundreds of protesters in Aleppo, Syria's commercial hub, were beaten back on Thursday by baton-wielding security forces, activists said.

And an activist said on condition of anonymity that "explosions were heard Friday in the Latakia district of Raml al-Shamali," without elaborating.

On Thursday, the opposition also turned up the heat on Assad, announcing the creation of a "national coordination committee" of exiled dissidents and opponents at home to push for democratic reforms.

The announcement came after about 160 dissidents, several of whom have spent years in jail, gathered in Damascus earlier in the week, vowing to press ahead with a "peaceful uprising for freedom and democracy and pluralism to establish a democratic state through peaceful means."

"There are two ways forward -- the first a clear and non-negotiable move to a peaceful transition to democracy which would rescue our country and our people," opposition activist Munzer Khaddam told the meeting.

"The alternative is a road that leads into the unknown and which will destroy everyone," he said.

They demanded the right to demonstrate peacefully, the release of political prisoners, freedom of the press, the safe return of refugees and moves to prevent foreign intervention.

The crackdown comes in defiance of repeated global condemnation and warnings from Western powers to Syria to show restraint and despite new US sanctions against regime pillars and Syria's ally Iran.

The Observatory says 1,360 civilians have been killed since mid-March and that 343 security force personnel have also died. Thousands have been arrested.