Meanwhile, Britain summoned the Syrian ambassador in coordination with other European nations, warning of "further measures" if it fails to stop the crackdown on protesters.
Activist Nawar al-Omar said Fuad Rajab, 40, was hit by a bullet to the head when security forces fired to break up a demonstration in the central city of Homs. Another person was also killed, but there were no immediate details.
In Hama, the army used batons, tear gas and water cannons to scatter anti-regime rallies, but protesters succeeded in ripping down a town hall portrait of the president, an activist said.
And in the southern flashpoint town of Daraa, security forces fired warning shots to disperse thousands of anti-regime demonstrators, another activist said.
The gunfire erupted as thousands of demonstrators took to Daraa's streets after weekly Muslim prayers, said the activist in the town that was the scene of a massive 10-day military operation that ended last week.
Thousands also marched the northern, mostly Kurdish regions of Qamishli, Derbassiye and Amuda, as well as in the Damascus suburb of Saqba, where security forces tore down anti-regime banners, activists told AFP.
After several days of sweeping arrests in protest hot spots, soldiers and security services were deployed in a massive show of force for the latest showdown with demonstrators across Syria on the Muslim weekly day of prayers.
Louai Hussein, a writer and leading activist, said earlier the protests would go ahead as planned following midday prayers in mosques, after Assad's office promised him that security forces would not shoot at demonstrators.
In a message posted on his Facebook page, Hussein said senior Assad adviser Bouthaina Shaaban had "told me during a telephone conversation that strict presidential orders were given not to fire on the demonstrators."
"All of those who violate these orders will assume full responsibility," he quoted Shaaban as saying.
The activist went on to call for "peaceful protests, regardless of the behaviour of the security services."
Meanwhile, Shaaban announced that the regime planned to start "a national dialogue" on topics including political pluralism, elections and the media next week with Hussein and other activists, according to Al-Watan, a daily close to the regime.
And Information Minister Adnan Mahmud said the Syrian army on Friday started to pull out of the coastal province of Banias where it deployed in force last week to curb anti-regime protests.
"After having ensured a return of security, the army divisions have started a gradual withdrawal from Banias and its province," where they were deployed last Saturday, he said.
The Syrian Revolution 2011, a Facebook group that has been a driving force behind the protests, called for a "Free Women Friday" in support of arrested women demonstrators.
Four women were killed during protests on May 7. Several more have been arrested, particularly in Damascus and the Mediterranean coastal city of Banias, where they marched calling for the release of detained relatives, activists said.
In London, Foreign Office political director Geoffrey Adams urged Syria to "stop the killing of innocent protestors immediately, and to release all political prisoners", a statement said.
Adams urged Syria to "stop the killing of innocent protestors immediately, and to release all political prisoners."
A Foreign Office spokesman told AFP it was "part of a coordinated EU move" but did not say how many other countries were involved. Five EU nations summoned the Syrian ambassadors to their countries in April.
Russia cautioned earlier against foreign intervention in Syria that could repeat the "Libya scenario," after the United States warned that Assad's regime would face more international pressure over its bloody crackdown on protests.
Syria, one of the most autocratic countries in the Middle East, has been rocked by two months of unprecedented popular protests inspired by revolts that ousted strongmen in Tunisia and Egypt.
Up to 850 people have been killed and at least 8,000 arrested since the protest movement emerged in mid-March, human rights groups say.
The regime has routinely blamed the deadly violence on "armed terrorist gangs."