It comes ahead of a planned meeting with President Bashar al-Assad.
Foreign Minister Walid Muallem, who held talks with Mr Brahimi on his arrival, said he backed the mission.
Meanwhile, in an interview with the BBC, former envoy Kofi Annan warned there could be no "military solution" to the conflict.
Thousands of people have been killed in Syria since the unrest began in 2011.
On Thursday, Syrian government forces carried out air strikes on Syria's commercial capital, Aleppo, activists said.
Clashes have been reported in the western and southern parts of the city, as well as in several parts of Damascus.
The reports have not been independently verified.
After his arrival in Damascus on Thursday, Mr Brahimi said: "There is a crisis, no-one denies it... It is a crisis which is deteriorating, and no-one disagrees with the need to stop the bloodshed and restore harmony."
According to Syrian state media, Mr Muallem stressed that any initiative should "focus on the Syrian people's interest".
The UN-Arab League envoy also met Mohammed Reza Shibani, the Iranian ambassador to Syria. Tehran has been and remains a staunch supporter of Mr Assad.
Pro-Assad Addounia TV channel said Mr Brahimi would meet the president on Saturday, and not Friday as had previously been reported.
The envoy is due to meet a delegation from the opposition National Co-ordination Committee for Democratic Change (NCCDC), an umbrella group of leftist, Kurdish and independent political activists, with calls for dialogue with the government.
When he took over the post, Mr Brahimi said bringing peace to Syria would be "nearly impossible". He has described the bloodshed there as "staggering" and the destruction as "catastrophic".
He was appointed to the role in August after the resignation of Kofi Annan, who quit after his peace plan for Syria failed to affect the crisis.
Speaking to the BBC, Mr Annan said the world community must get its act together to resolve the Syrian conflict, describing the failure to do so as "shameful".
He also urged regional players to exert pressure both on President Assad and the rebels to settle the crisis peacefully.
"Left on their own, they will not go and talk," Mr Annan warned.
UN-Arab League envoy to Syria Lakhdar Brahimi, on his first mission to the country, is to meet an opposition group tolerated by the government.