Militants fired rocket-propelled grenades at the Central Bank building in Damascus and also attacked a police patrol in the capital, wounding four police, state television has reported.
It said the attack on the Central Bank by "an armed terrorist group" caused only slight damage, and security forces were chasing the attackers of the police patrol.
Activists in the capital reported hearing several explosions and gunfire.
Maj Gen Robert Mood, a Norwegian, was appointed head of the observer mission by UN chief Ban Ki-moon. One-hundred monitors should be in the country by mid-May, said mission spokesman Neeraj Singh. It is unclear when or if the full contingent of 300 monitors will deploy to Syria.
Jakob Kellenberger, president of the International Committee of the Red Cross, said that while he is still hopeful, "unfortunately I am also aware how much this plan is at risk".
"That's why it's especially important for this mission to expand quickly," Mr Kellenberger told the Swiss newspaper Der Sonntag. He met with Syrian leaders earlier this month.
The head of the UN observer mission in Syria has called on President Bashar Assad and the country's opposition to stop fighting and allow a tenuous ceasefire to take hold.
Maj Gen Robert Mood spoke after arriving in the Syrian capital Damascus to take charge of an advance team of 16 UN monitors trying to salvage an international peace plan to end the country's 13-month crisis.
Under the plan, a ceasefire is supposed to lead to talks between Assad and the opposition on a political solution to a conflict that has killed more than 9,000 people.
Mr Mood told reporters that the 300 observers the UN has authorised for the mission "cannot solve all the problems" in Syria, asking for co-operation from forces loyal to Assad as well as rebels seeking to end his rule.
"We want to have combined efforts focusing on the welfare of the Syrian people," he said. "True cessation of violence in all its forms."