The Syrian League for the Defence of Human Rights blamed Assad for the deadly repression of dissent and said he should be "tried for crimes against humanity," in a statement received by AFP in Nicosia.
The watchdog said 3,482 people, including 212 children and 99 women, have been killed since mid-March and 4,232 wounded, adding that more than 191 deaths "were the result of torture in detention centers."
UN human rights chief Navi Pillay said at the weekend that more than 3,000 people, including 187 children, have been killed in the regime's crackdown.
She warned that Syria risked "a full-blown civil war."
In Tuesday's violence, three civilians were shot dead and dozens wounded when security forces opened fire in the Daraa town of Herak, according to the Britain-based Syrian Observatory for Human Rights.
The Local Coordination Committees, an activist network spurring protests, said demonstrators had taken to the streets there to protest the arrest earlier Tuesday of a local cleric, Sheikh Wajih Kaddah, by pro-regime thugs.
The LCC reported tank fire and said electricity was cut throughout Herak.
The Observatory also reported that a sniper killed an intelligence officer in Idlib province bordering Turkey as armed resistance to the security forces spread, while search operations in the flashpoint central province of Homs killed one person and wounded 15 people.
Around the capital, "several towns were targeted by the fiercest security operations since the start of the revolution" the Observatory said.
"The army and the security services have imposed a complete blockade and snipers are posted on tower blocks," it added.
"Residents are being prevented from getting to their places of work or study and dozens of young people were arrested."
Troops also detained 25 people in Daraa and 15 in the town of Saraqeb in Idlib province, the watchdog added.
In Homs province, troops killed one person in the town of Qusayr and wounded nine in villages during search operations for army deserters, the Observatory said.
"Convoys of armoured cars criss-crossed the streets of Qusayr, firing on anything that moved and particularly at motorcycles."
On Monday, the Observatory said troops killed 27 people, most of them civilians but some of them police, in Homs city.
In Ankara, Turkish Foreign Minister Ahmet Davutoglu received Syrian opposition leaders for their first formal talks and urged them to forge a united front in pursuit of a peaceful transition from Assad's iron-fisted rule, a Turkish diplomat said.
"Turkey advised the (Syrian National Council) to be unified and work together to proceed towards democratic and peaceful transition in Syria ... because the current situation cannot be sustained," the diplomat said.
The SNC, the largest and most representative Syrian opposition grouping, was founded in Istanbul at the end of August and numbers 140 members, half of them living in Syria.
Ankara had developed close ties with Assad's regime over the past decade but has expressed growing frustration with the president's failure to address popular demands for reform.