An ultimatum set by Syrian authorities came as activists planned fresh anti-government demonstrations following the deaths of dozens of people in weekend protests.
In its statement, the interior ministry said "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 over to the competent authorities."
The statement also called on Syrians to "supply information about saboteurs, terrorists and arms caches... 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 death 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.
According to the opposition Syrian Revolution 2011 website, security forces on Monday at dawn also entered the Kafar Nubbol area, 320 kilometres (200 miles) north of Damascus, and took over houses and arrested 26 people.
The site urged Syrians across the country to mobilise every day at noon in solidarity with Daraa and all "besieged towns."
"We say to this regime: 'The court of the people will judge you'," it said.
Hundreds of dissidents were arrested on Sunday, including in Daraa and the besieged Damascus suburb of Douma, after dozens of people were killed in weekend protests, activists said.
Human rights groups say the civilian death toll from unprecedented demonstrations that erupted on 15 March has topped 580.
French Foreign Minister Alain Juppe said on Monday that President Bashar Al-Assad's regime will fall if it continues its bloody crackdown.
"If the regime perseveres down this path, it will fall, one day or another, but it will fall," Juppe told Europe 1 Radio.
"Today there is this great hope for freedom and democracy. You must take this into account and putting it down by firing live rounds into crowds is unacceptable, whichever country does it," he said.
British Prime Minister David Cameron on Sunday denounced the "disgraceful" crackdown and urged more global pressure against Damascus, although Turkish Foreign Minister Ahmet Davutoglu warned against foreign military intervention.
The United States has blocked the assets of Assad's brother Maher, who commands the feared Fourth Armoured Division, as well as top officials and Syria's intelligence services.
The European Union is also preparing a raft of sanctions, including an arms embargo.
"At least 356 people were arrested today [Sunday] across Syria, including in Daraa, Douma, Latakia and Qamishli," an activist told AFP by telephone.
He said demonstrations took place in the central city of Homs. A protest was also held in the coastal city of Latakia and a candlelit vigil in Banias.
Troops in tanks backed by other armoured vehicles on Sunday cruised Daraa streets, shooting to keep residents indoors and arresting men aged 15 and over, an activist from the town told AFP.
"Since early morning the army and security forces have been combing neighbourhoods one by one and making sweeping arrests. Hundreds have been arrested since Friday," activist Abdullah Abizad said by telephone.
In Douma, "the army has tightened the siege and has a list of 200 names of people it wants to arrest," another activist said.
Activists said many people in Douma and Daraa live off the land and have been relying on what they grow.
In Daraa, "nothing is coming in. People there grow a lot of tomatoes and zucchini and they are making do with what they have. The situation is critical but there is no famine."
The Syrian Revolution 2011, the driving force behind the protests, vowed in a Facebook statement that "we will only kneel before God," and gave a daily schedule of protests for the week in solidarity with Daraa and Douma.
The army said it entered Daraa on 25 April 25 at the request of residents to rid them of "terrorist gangs" responsible for a spate of killings and vandalism."
The Committee of the Martyrs of the 15 March Revolution, which has been keeping a tally of the dead, put the toll since the start of protests at 582 civilians.
The London-based Syrian Observatory for Human Rights said 86 army and security forces personnel have also been killed.
The arrests are taking place despite the lifting on 21 April of almost five decades of emergency rule and the abolition of the repressive state security court.