British Prime Minister David Cameron denounced Syria's "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 assets of President Bashar al-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 preparing a raft of sanctions, including an arms embargo.
"At least 356 people were arrested today 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, where protesters chanted "the people demand the fall of the regime" in the Khaldiyeh area near Nur mosque.
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.
A young man told AFP how he escaped on Sunday from Douma at "great risk" using back roads. "It was very difficult and very dangerous. I had to avoid all the checkpoints."
"People are afraid to leave their homes but they are beginning to feel the pinch. There are shortages of food, baby milk and other basic stuff," he said.
According to him, the price of bread has shot up fivefold for a 1.5-kilogramme pack (about three pounds) of flat pita-type bread to 75 Syrian pounds (1.5 dollars)
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, a 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 April 25 at the request of residents to rid them of "terrorist gangs" responsible for a spate of killings and vandalism.
"The manhunt for terrorist groups has led to the death of six of them and the arrest of 149 wanted people as well as the seizing of a quantity of arms," according to a military spokesman.
He said one soldier was killed and seven others wounded on Saturday in Daraa, where water and power have been cut since between 3,000 and 5,000 troops backed by tanks stormed the town at dawn last Monday.
Abizad said living conditions were deteriorating and residents were cowering indoors.
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.
Activists say that more than 66 people were reported killed on Friday alone in a "day of rage" against the regime. The authorities said nine members of the security forces were shot dead by "terrorist groups."
Scores of prominent human rights and opposition militants are also being rounded up despite the lifting on April 21 of almost five decades of emergency rule and the abolition of the repressive state security court.
Lawyer Hassan Ismail Abdel Azim and communist party leader Omar Kashash were arrested on Saturday when 11 women who took part in a Damascus protest were also detained, according to rights groups and activists.
Activists said countrywide protests would begin with demonstrations for Daraa on Sunday and around Damascus on Monday.
Rallies are planned on Tuesday in the northern towns of Banias and Jableh, Wednesday in Homs, Talbisseh and in Tall Kalakh on the border with Lebanon, and nationwide night vigils on Thursday.
Pressure against the embattled president from home and abroad increased as more members of Assad's ruling Baath party resigned to protest at the security crackdown, a new list of 138 names showed.
Across the border in Jordan, more than 200 Syrians took part in a demonstration at which an effigy of Assad was hanged outside their embassy in Amman on Sunday.