Activists and witnesses said demonstrations broke out after the main Friday prayers in cities across the country of 20 million people, from Banias on the Mediterranean coast to Qamishly in the Kurdish east.
The bloodiest confrontation took place in the central city of Homs where 15 protesters were killed, activist Ammar Qurabi said. Syrian state television said an army officer and four police were killed in Homs by a "criminal gang".
International criticism has mounted against Assad, who has gone on the offensive to maintain his family's four-decade grip on power and crush demonstrators demanding freedom.
European Union governments agreed on Friday to impose asset freezes and travel restrictions against Syrian officials responsible for the violent repression, which rights campaigners say has killed more than 580 people.
Officials give a lower death toll and say half the fatalities have been soldiers and police, blaming "armed terrorist groups" for the violence. They say demonstrators are few in number and do not represent the majority of Syrians.
It was not immediately clear if Assad himself would be targeted under the sanctions, which follow last week's EU agreement in principle to impose an arms embargo on Syria. The measures will be approved on Monday if no member state objects.
Assad's security forces and troops, which stormed the city of Deraa last week, have prevented demonstrators establishing a platform such as Egypt's Tahrir Square by blocking access to the capital Damascus. But every week protesters have used Friday prayers to launch fresh marches.
"The people want the overthrow of the regime," shouted 2,000 demonstrators in the Damascus suburb of Saqba, demanding the release of hundreds of relatives arrested by security forces in the last few days, a witness said.
Footage released on the Internet and aired on Al Jazeera television showed protesters in several towns and cities echoing the same calls for freedom and change of leadership.
'Syrian people will not back down'
Tanks deployed in the Damascus district of Barzeh and in Homs.
In Hama, where Assad's father brutally suppressed an armed Islamist uprising in 1982, a rights activist said security forces shot dead six demonstrators when they fired at a protest.
The London-based Syrian Observatory for Human Rights said a protester was killed in Latakia and three others wounded.
There were also protests in the Damascus district of Midan, the suburb of Daraya and towns of Zabadani and Tel Kelekh near the Lebanon border. Activist Wissam Tarif said live ammunition was fired in at least at four demonstrations.
Despite the harsh crackdown, protesters appear determined to maintain demands for an end to years of repression, arrests without trial and corruption by the ruling elite.
"The Syrian people will not back down after the country's budding youths were killed in their hundreds," said Montaha al-Atrash of the Syrian human rights organisation Sawasiah.
Opposition leader Riad Seif, who helped initiate a peaceful movement seeking political freedoms and democracy 10 years ago, was arrested at one of Friday's protests, his daughter said.
Authorities also arrested on Thursday prominent Damascene preacher Mouaz al-Khatib, a major figure in the uprising, human rights campaigners said on Friday.
A Western diplomat said 7,000 people had been arrested since the demonstrations broke out on March 18 in Deraa.
The United States, which sought for the last few years to engage Damascus and loosen its anti-Israel alliances with Iran and militant groups Hezbollah and Hamas, imposed further targeted sanctions against Syrian officials last Friday.
Last week, Assad ordered the army into Deraa, cradle of the uprising that began with demands for greater freedom and an end to corruption and is now pressing for his removal.
An ultra-loyalist division led by his brother Maher shelled and machinegunned Deraa's old quarter on Saturday, residents said. The United States condemned the assault as "barbaric".
Syrian authorities said on Thursday the army had begun to leave Deraa, but residents described a city still under siege.
"With our soul and blood, we will sacrifice for you, Deraa", chanted 20,000 protesters in nearby Jassem on Friday.
Thousands more converged on the town of Tafas, 12 km (8 miles) northwest of Deraa, which remains encircled by tanks, carrying placards with the word "leave".
Aid workers from the Red Cross and Red Crescent delivered their first emergency relief supplies to Deraa on Thursday, bringing drinking water, food and first aid materials. They had no immediate information on casualties in the city.
Human Rights Watch cited figures from Syrian rights groups saying 350 people had been killed there. It urged authorities on Friday to "lift the siege" on the city and to halt what it called a nationwide campaign of arbitrary arrests.
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