Earlier, the source said the Syrian army had been strengthening its forces there for the past three days.
Ar-Rastan residents have toppled a statue of the late Syrian president Hafez al-Assad, who was succeeded on his death in 2000 by his son, current president Bashar al-Assad.
In a phone call Wednesday, Ban appealed to Assad to end the deadly clampdown, to allow a UN aid team into worst-hit towns and to cooperate with a UN Human Rights Council investigation into the violence, a spokesman said.
"The secretary general reiterated his calls for an immediate end to violence against and mass arrests of peaceful demonstrators," UN spokesman Martin Nesirky said in a statement.
The UN leader said there had to be "full and early implementation of all the reform measures" promised by Assad's government "and emphasised the importance of engaging a genuine inclusive dialogue and a comprehensive reform process."
Activists said more than 1,000 people had been arrested across Syria so far this week, as around 150 students held a brief sit-in at the university in the southern flashpoint town of Daraa, which has been besieged by the army for 10 days.
A military spokesman said later on state television, however, that the army was "on the verge of completing its mission (in Daraa), having achieved most of its objectives."
The committee coordinating the anti-government protests in a string of cities said: "We must continue our peaceful revolution throughout Syria until we achieve the freedom we demand."
The cities include Daraa, the epicentre of protests, Banias on the Mediterranean coast and the central industrial city of Homs.
The opposition said the "live ammunition fired into the crowds has not stopped the young people from demonstrating.
"The crowds are only growing in size and momentum. The government’s fierce campaign of arbitrary mass arrests will not succeed where their bullets have failed," it said in a statement obtained by AFP.
"Having failed to stop the protests and demonstrations in Syria through their various means of oppression, besieging cities, censoring and cutting off communications, and even firing live ammunition, ... the Syrian government has, in recent days, intensified their effort to arrest citizens," it said.
At least 500 people are being arrested every day on average, it added.
The civilian death toll from the unprecedented demonstrations in Syria has already topped 607 since March 15, according to Syria's Insan human rights group, which said as many as 8,000 people were now listed as arrested or missing.
The government of embattled President Assad has persistently blamed the violence on "armed criminal gangs" and portrayed the protest movement as a conspiracy.
As a wave of arrests intensified, an online post by the Syrian Revolution 2011 Facebook group had urged "Syrians in all regions to gather from Tuesday evening in all public places to organise sit-ins" round the clock.
On Wednesday around 150 students shouting "With our soul and blood we defend Daraa; lift the siege in Daraa" held a sit-in at the town's university, which was quickly broken up by security forces, an activist said.
Amnesty International said a "wave of arrests of anti-government protesters intensified over the weekend."
"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," it said.
The United States has denounced measures used by Syria to put down the anti-regime protests as "barbaric" and amounting "to the collective punishment of innocent civilians."
President Nicolas Sarkozy told L'Express magazine France was going to "push for the adoption of the harshest possible sanctions," while his Foreign Minister Alain Juppe said Paris wanted to have Assad named in EU sanctions.
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.
Last week, Washington froze the assets of top officials, including Assad's brother, Maher, who commands the feared Fourth Armoured Division.