The secretary-general said in a statement that unarmed UN military observers in Syria had reported a "continued presence of heavy weapons, military equipment and army personnel in population centers." Ban said he was "deeply troubled" by that.
The statement from Ban's press office said he considered that a "contravention of the Syrian Government's commitments to withdraw its troops and heavy weapons from these areas" and demanded that Damascus comply with its pledge without delay.
A shaky ceasefire was implemented earlier this month under a peace plan brokered by UN-Arab League envoy Kofi Annan. Syrian Foreign Minister Walid al-Moualem wrote to Annan on Saturday to inform him that Damascus had withdrawn heavy weapons and troops from cities, according to Syria's U.N. envoy, Bashar Ja'afari.
The UN Security Council unanimously adopted a resolution on Saturday that authorized an initial deployment of up to 300 unarmed military observers to Syria for three months to monitor the truce.
Only 15 are in place so far out of a team to be led by Norwegian General Robert Mood.
Despite the truce, daily fighting has continued. More than 9,000 people have died in Syria during 13 months of fighting sparked by a popular uprising against President Bashar al-Assad.
An explosion on Wednesday killed 16 people in the city of Hama. Syria blamed "terrorist" bomb-makers for the blast, while the grass-roots opposition group, Local Coordination Committees, said it was a military rocket that killed more than 50 people.
"The Secretary-General is gravely alarmed by reports of continued violence and killing in Syria, including shelling and explosions in various residential areas as well as armed clashes," Ban's statement said.
"This situation is unacceptable and must stop immediately," it said.