Syrian security forces killed at least 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 people since mid-March.

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

Qorabi, who runs the National Organisation of Human Rights and is based in Egypt, said by telephone that a seventh person was killed on Friday in an unrelated drive-by grenade attack.

State television gave a conflicting toll, saying gunmen killed one demonstrator in Damascus and two people in Homs, one a policeman.

Waves of protesters flooded the streets nationwide to demand the fall of the regime, with varying reports putting the turnout in the central city of Hama alone at more than half a million.

The head of the Syrian Observatory for Human Rights, Rami Abdel Rahman, spoke of 500,000 protesters and said this was "the biggest 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 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.

Hama has a bloody past. In 1982, an estimated 20,000 people were killed when the army put down an Islamist revolt.

Demonstrations also gripped the protest hub of Homs where one activist said "more than 100,000 people" protested in several districts as tanks were deployed.

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 weekly 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.

State television reported pro-regime demonstrations in the northern commercial hub of Aleppo and in Suweida, in the south, with people chanting "God, Syria, Bashar and that's it."

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

Meanwhile 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 the Facebook group, The Syrian Revolution 2011 group, which called on people to rally, 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.

On Thursday, the opposition announced 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 Monday in Damascus, vowing to press ahead with a "peaceful uprising for freedom and democracy and pluralism to establish a democratic state through peaceful means."

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