In a statement, the interior ministry told "citizens who have participated in or committed unlawful acts such as bearing arms, attacking security or spreading lies to surrender by May 15 and hand their weapons in to the competent authorities."
It urged Syrians to "supply information about saboteurs, terrorists and arms caches" pledging "they will be spared any subsequent legal consequences."
A military spokesman on Monday announced the arrest of 499 people in the southern flashpoint town of Daraa, a week after thousands of troops backed by tanks swooped on the town to crush protests.
The spokesman also announced the deaths of two members of the security forces "as well as 10 terrorists." Eight soldiers were wounded and five gunmen waiting in ambush were arrested, the military added.
Security forces and the army continue to "pursue terrorist groups and have arrested members of these groups who committed crimes and acts of sabotage in the city" of Daraa, state news agency SANA reported.
Quoting a military official it said large quantities of arms and ammunition were found hidden in various places in Daraa.
Meanwhile President Bashar al-Assad met visiting UAE Foreign Minister Sheikh Abdullah bin Zayed Al-Nahyan and told him "measures are being taken to overcome the current situation and strengthen the process of reforms in all fields," SANA said.
According to the opposition Syrian Revolution 2011 website, security forces at dawn on Monday entered the Kafar Nubbol area, 320 kilometres (200 miles) north of Damascus, and took over houses and arrested 26 people.
Raids were also carried out at dawn in Zabadani and Madaya, two summer resorts northwest of Damascus, where security forces arrested 147 people, the rights group Insan said.
"Those detained were beaten and insulted in front of their relatives and their cell phones and computers were seized," Insan said in a statement.
On Sunday troops and security forces arrested more than 365 people, namely in Daraa and the Damascus suburb of Douma, the northwestern coastal city of Latakia and Qamishli in the northeast, activists said.
The Syrian Revolution 2011 site, a driving force behind the protests, urged Syrians nationwide to mobilise every day at noon in solidarity with Daraa, which has been sealed since Monday by the army, and all "besieged towns."
"We say to this regime: 'The court of the people will judge you'," it said.
SANA reported that 600 tonnes of flour had been delivered to Daraa, where there are huge shortages of food, medicine and baby milk, activists say.
Also on Monday security forces dispersed a group of around 150 women who marched in central Damascus in support of Daraa and arrested a woman journalist, actress Fadwa Suleiman told AFP.
"The security forces ordered us to stop, they beat up some women and arrested a Syrian woman journalist who argued with them after they seized her camera," she said.
Assad's government has persistently blamed the violence on "armed criminal gangs" while the president has portrayed the protest movement launched on March 15 as a conspiracy.
The army said it entered Daraa on April 25 at the request of residents to rid them of "terrorist gangs" responsible for a spate of "killings and vandalism."
Human rights groups say the civilian death toll from unprecedented demonstrations that erupted on March 15 has topped 580, and Insan said 2,130 arrests have been verified since March 15.
On Monday French Foreign Minister Alain Juppe warned that Assad's regime was bound to fall if it continued its bloody crackdown.
"If the regime perseveres down this path, it will fall, one day or another, but it will fall," Juppe said.
Also on Monday Al-Jazeera television demanded information about one of its journalists, Dorothy Parvez, who has been missing since landing on Friday in Damascus.
Parvez, 39, who holds American, Canadian and Iranian citizenship, is the latest journalist to be reported missing in Syria.
Al-Jazeera has been accused, along with other satellite channels, by the Syrian authorities of exaggerating anti-regime protests.
A Jordanian, Raad Kawar, has also been detained by Syrian authorities since April 19 while on way to Amman upon return from Beirut, his family and the Jordanian Foreign Ministry said Monday.
The United States has blocked assets of Syrian officials, including those of Assad's brother Maher, who commands the feared Fourth Armoured Division, while the European Union is also preparing a raft of sanctions.
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