Thousands took to the streets demanding the overthrow of President Bashar al-Assad after morning prayers marking the end of the Islamic month of Ramadan.

Activists said six were killed in the southern province of Deraa, including three in the town of al-Harra.

Several protesters were also reportedly injured in the suburbs of Damascus.

State television, meanwhile, broadcast pictures of the president attending prayers in one of the capital's mosques and taking coffee and cakes with fellow worshippers, reports the BBC's Jim Muir in Beirut.

There were impromptu demonstrations against Mr Assad nationwide on Tuesday as people spilled out of mosques after morning prayers.

But much of the focus was on cemeteries, where it is customary on the first day of Eid to visit the graves of relatives, says our correspondent.

In the southern city of Deraa, activists said a "huge" protest formed as worshippers emerged from the al-Omari mosque - scene of a crackdown at the start of the uprising - and marched to the cemetery. The crowd was confronted by hundreds of security personnel and militiamen.

"They can shoot and kill as much as they want, we will not stop calling for regime change," one activist told the Associated Press by telephone.

At least three people were reported to have been killed in al-Harra, including a 13-year-old boy, when security forces opened fire to disperse a demonstration in the town, which is located to the north of Deraa.

The Local Co-ordination Committees, an activist group that documents and organises protests, said there were also large protests in many other towns and villages in Deraa province.

Two people were killed in Inkhil, while in Nawa, soldiers opened fire on worshippers who had gathered in the street, the group added.

In the Damascus suburb of Qaboun, a crowd marching towards a cemetery was surrounded by security forces, who opened fire. The Syrian Observatory for Human Rights said five people were critically injured.

Troops were also reported to have shot at protesters in the eastern city of Deir al-Zour, scene of a major assault by security forces at the beginning of Ramadan, when the government crackdown escalated.

"Instead of celebrating Eid, we were just out protesting. We will continue our revolution until it achieves the target - we don't want the regime anymore, we want to get rid of it," one Damascus resident told the BBC.

"We have been going out for five months, we always face the live ammunition with our bare chests, and some people are saying: 'For how long are we going to keep this up?'

"I think the international community should take its full responsibility against the Syrian regime, to take all practical measures to stop it and to protect the civilians," he added.

On Tuesday, EU foreign police chief Catherine Ashton expressed her "continued deep concern about the violence perpetrated by the Syrian regime against peaceful demonstrators, human rights activists, and the Syrian people at large".

"She renews her unequivocal condemnation of the brutal repression," said a spokesman, a day after EU states agreed to ban oil imports from Syria, a measure that is expected to be formally adopted this week.

Later, the US announced it had frozen the assets of Syrian Foreign Minister Walid Muallem, Bouthaina Shaaban, Mr Assad's adviser and spokeswoman and the Syrian ambassador to Lebanon, Ali Abdul Karim Ali.

"We are bringing additional pressure to bear today directly on three senior Assad regime officials who are principal defenders of the regime's activities," said David Cohen, the treasury department's under-secretary for terrorism and financial intelligence.

The UN has said more than 2,200 people have been killed since pro-democracy demonstrations began in mid-March. Syria's government has blamed "armed criminal gangs" for much of the unrest.

Access to Syria has been severely restricted for international journalists and it is rarely possible to verify accounts by witnesses and activists.