Ban was particularly concerned about reports of 17 people gunned down in Daraa and another 10 killed in surrounding villages Friday during anti-regime demonstrations.
"He said the killing of peaceful demonstrators was unacceptable and should be investigated," the UN said in a statement.
"The secretary general reiterated the duty of governments to protect civilians and respect the rights and freedoms of the population including the right of free speech and peaceful assembly," the statement said.
Ban expressed encouragement at the Syrian president's "intention to investigate" the killings.
"He also noted there were reports that demonstrators had used violence and killed security personnel. The secretary general underlined that violence from any side was deplorable."
Ban called for the release of detained demonstrators "as soon as possible" and said the country's problems can only be solved through "an immediate dialogue and comprehensive reforms."
On Saturday, Syrian security forces shot at protesters in Daraa, an activist said, as a huge crowd buried the dead from the bloody crackdown Friday. Two people were wounded.