Amnesty International meanwhile released a statement on "first-hand reports of torture" from detainees held in Syria.
As a wave of arrests intensified, a Facebook post by the Syrian Revolution 2011 website urged "Syrians in all regions to gather from Tuesday evening in all public places to organise sit-ins" round the clock.
The National Organisation for Human Rights in Syria said more than 1,000 people had been arrested in two days.
"There has been an insane intensification of arrests in towns. The authorities are arresting anyone who wants to demonstrate, especially writers, intellectuals and activists known to be demanding reform," it said.
Amnesty also said a "wave of arrests of anti-government protesters intensified over the weekend."
"Detainees who were recently released told the organisation of beatings and harsh conditions in detention, raising fears for the safety of hundreds of others being held, including at least 499 people who were arrested on Sunday in house-to-house raids in the southern town of Daraa," said Amnesty.
"The use of unwarranted lethal force, arbitrary detention and torture appear to be the desperate actions of a government that is intolerant of dissent and must be halted immediately," said Amnesty's Middle East and North Africa deputy director Philip Luther.
The United States denounced measures used by Syria to put down seven weeks of anti-regime protests.
"These are quite frankly barbaric measures and they amount to the collective punishment of innocent civilians," State Department spokesman Mark Toner said in Washington.
He spoke specifically about Daraa, the epicentre of the protest movement launched March 15, which has been sealed by the army since April 25 when up to 5,000 troops backed by tanks rolled into the town.
French Foreign Minister Alain Juppe said Assad's government is losing legitimacy and EU sanctions should target the Syrian president.
Asked whether France wanted Assad to be specifically named in the measures being discussed in Brussels, Alain Juppe told reporters: "France wishes so."
"A government that kills its citizens because its citizens want to express themselves and install a real democracy loses its legitimacy," he said.
President Nicolas Sarkozy also told L'Express magazine: "For Syria we are going to push for the adoption of the harshest possible sanctions."
Israeli Defence Minister Ehud Barak also predicted that Assad's "brutality" towards the protesters will lead to the downfall of his regime.
The European Union on Friday launched preparations for an embargo on the sale to Syria of weapons and equipment that might be used for internal repression. Advisers met on Monday and Tuesday to fine-tune the sanctions.
But diplomats told AFP that while there was general agreement on slapping an arms embargo on Syria, there were divisions concerning targeted measures against Syrian officials.
Washington last week froze the assets of top officials, including Assad's brother Maher who commands the feared Fourth Armoured Division.
On the ground some 3,000 people demonstrated in the northern port and oil terminal of Banias, another centre for protests against Assad's government, demanding the lifting of the siege of Daraa, an activist said.
Activists posted footage on YouTube of protests in Homs and in the Midan district of Damascus. "No to violence, no to sabotage, no to unemployment" read a banner at one demonstration in the Bab Sbaa quarter of Homs.
Protests also took place in Hama and in the Jassem area near Daraa.
"Important arrests in Daraa today (Tuesday) and yesterday according to lists: people aged between 18 and 40 interrogated in a Daraa stadium, at least 1,000 detained," a human rights activist in Damascus said.
Daraa was reported to have water and electricity again on Tuesday, except for the Al-Omari mosque area which was the scene of clashes.
The army said it had entered Daraa last week at the request of residents to rid them of "terrorist gangs" responsible for a spate of "killings and vandalism."
The international Red Cross urged Syria to lift restrictions on access to casualties in Daraa.
"The violence has resulted in a large number of casualties and we fear that if the situation worsens more lives will be lost," said Marianne Gasser, head of the ICRC delegation in Damascus.
Meanwhile, the International Crisis Group warned that Syria was "quickly going beyond the point of no return.
"By denouncing all forms of protest as sedition, and dealing with them through escalating violence, the regime is closing the door on any possible honourable exit to a deepening national crisis," the think-tank said in a report on Tuesday.
The interior ministry announced Monday a 15-day deadline for people who had committed "unlawful acts" to give themselves up and urged Syrians to "supply information about saboteurs, terrorists and arms caches."
Assad's government has persistently blamed the violence on "armed criminal gangs" and has portrayed the protest movement as a conspiracy.
The Insan human rights groups said the civilian death toll from the unprecedented demonstrations in Syria has topped 607.
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