Brahimi spoke after rebels were reported to have advanced into a key district of the northern city of Aleppo, where activists said at least 11 people were killed in a strike by a helicopter gunship.
Brahimi later met Syrian Foreign Minister Walid Muallem, "who said he was committed to ensuring the success of Mr. Brahimi's mission," the peace envoy's spokesman Ahmad Fawzi said.
During the talks Brahimi emphasised that "he would spare no effort to help find solution to the crisis," he said.
"His only masters in this endeavour were the Syrian people whose welfare and security were his prime concern. He has come to Damascus to listen and would also be meeting with representatives of the opposition and civil society," he added.
Fawzi had said that Brahimi would be meeting President Bashar al-Assad. On Friday he is due to meet members of opposition groups tolerated by the Syrian regime.
Brahimi was accompanied by Mokhtar Lamani, who will remain in Damascus to assume his new functions as head of office for the Joint Special Representative for Syria in the city.
Earlier Moallem's deputy, Faisal Muqdad said: "We trust that Brahimi has a general understanding of the developments and of the way to solve problems despite the complexities. We are optimistic and we wish Brahimi success."
However, the veteran Algerian diplomat highlighted to Arab League envoys in Cairo this week that he knows he faces an uphill struggle, with no sign of a lull in the violence.
He told the envoys that "he was approaching the crisis in Syria with his eyes open and the full knowledge that it was an extremely difficult task," a UN spokeswoman said.
In Brussels on Thursday, Egyptian President Mohamed Morsi reiterated that Assad must step down because "a president that kills his own people is not acceptable."
British Foreign Secretary William Hague, visiting Baghdad, told reporters the Damascus regime is "doomed, that it is not possible for it to survive, and so many crimes (have been) committed that it should not survive."
French Defence Minister Jean-Yves Le Drian said in Beirut that Paris will not send weapons to the Syrian opposition, despite repeated calls by rebels for arms.
"Things are very clear: on the question of supplying weapons, the answer is no. France does not supply and will not supply the Syrian opposition with weapons," he said.
On the ground, rebels and troops battled for control of the strategic Midan district of central Aleppo, which opens the way to the main square, with fighting raging around two police stations, residents said.
Rebels captured the police stations at dawn but were repelled by the army, residents said, adding that the insurgents fought their way back into the area and clashed fiercely with troops as the army tried to dislodge them again.
-- 'One of the worst days of our lives' --
An AFP journalist reported columns of black smoke hanging over the city, scene of some of the country's heaviest violence since fighting erupted there on July 20.
Warplanes fired at several districts from high altitude in a bid to stay out of range of rebel weapons.
"Today is one of the worst days we've lived," Mariam told another AFP correspondent in the city, as she rushed to treat wounded patients at a makeshift field hospital in the western neighbourhood of Saif al-Dawla.
"Here we have the proof that the army's only goal is to indiscriminately kill as many civilians as possible."
Most of the wounded brought to the field hospital were woman and children hit by shelling as they were out on the streets, the AFP correspondent reported.
The Syrian Observatory for Human Rights said several rebel-held districts of Aleppo were bombarded, with at least 11 people killed when a helicopter gunship targeted a crossroads in Tariq al-Bab.
It did not say whether the victims were rebels or civilians, but distributed video footage showing several bodies, some bloodied and others badly burned.
"The Free Syrian Army has already succeeded in forcing planes to fly at a higher altitude -- making their strikes less accurate -- and to limit the number of flights from certain key airports," FSA spokesman in Damascus province, Ahmed al-Khatib, told AFP via Skype.
Violence nationwide on Thursday killed at least 57 people, most of them civilians, according to the Observatory, which says that more than 27,000 people have been killed since the uprising against Assad's rule erupted in March last year.
One of Thursday's victims was an Armenian man shot dead by a sniper in Midan, the Observatory said, while seven people thought to be anti-regime fighters died in the south Damascus district of Sayyida Zeinab.
In neighbouring Lebanon, Maronite Christian Patriarch Bishara Rai said Pope Benedict XVI will call on the world to stop arming belligerents in the crisis when he begins a three-day visit to Syria's neighbour on Friday.