Annan, who is an envoy for both the United Nations and the Arab League on Syria, is in talks with the government and opposition representatives, the United Nations said.
"The hard part lies ahead, a truly Syrian-led and -owned political dialogue to address the legitimate concerns and aspirations of the Syrian people," the spokesperson added.
The first group of unarmed observers arrived in Syria earlier this week.
Whether the observer mission will have any effect is another question. U.N. Secretary-General Ban Ki-moon told the Security Council in a letter that Syria has failed to implement nearly every aspect of a six-point peace plan since the April 12 cease-fire, The New York Times reported Thursday.
The United Nations had been negotiating for a 300-member mission.
In Paris, U.S. Secretary of State Hillary Clinton, along with foreign ministers from the Middle East and elsewhere, gathered Thursday for a "Friends of Syria" discussion of the peace plan and ways to pressure Damascus.
Before the meeting, Clinton said Syrian regime backers must justify how they can let the bloodshed go on.
"The burden has shifted," Clinton told reporters in Brussels before flying to Paris for the meeting to boost pressure on Syrian President Bashar Assad's regime.
The onus has moved "not only to the Assad regime, but to those who support it, to be forced to explain why, after time and time again stating that they will end the violence, the violence continues," Clinton said.
Syrian security forces opened fire Wednesday on anti-regime demonstrators surrounding the four-wheel-drive vehicles of U.N. observers sent to monitor the cease-fire, activist groups said and amateur videos indicated.
The barrage of bullets -- in the suburban city of Arbeen near Damascus -- sent the observers' vehicles racing away, sirens blaring, and protesters scattering, running for cover, the amateur videos posted online showed.
"They are firing on demonstrators while the observers are visiting," a narrator in one video said.
A video taken before the shooting showed a pink handwritten sign taped to the back of one of the U.N. vehicles saying, "The killer keeps killing, the observers keep observing and the people keep rebelling."
Security forces and soldiers loyal to the Assad regime killed 46 people Wednesday in Homs, Idlib, Daraa, Hama, Deir Ezzor, Aleppo, Damascus and the Damascus suburbs, the opposition Local Coordination Committees of Syria said.
The state-run Syrian Arab News Agency said an "armed terrorist group" detonated an explosive device in the Idlib province that killed six Syrian law-enforcement officers. It said a sniper killed a police officer in Daraa.
The Assad regime says it has a right to respond to "terrorist" attacks, despite agreeing to the six-point peace plan brokered by U.N.-Arab League envoy Kofi Annan.
Notable deaths of 2014 [PHOTOS]