Ahead of the annual UN General Assembly starting on Tuesday, the UN and Arab League envoy is set to brief the UN Security Council behind closed doors on his talks in Damascus.
Brahimi discussed Syria with UN chief Ban Ki-moon on Saturday and both agreed that the 18-month crisis was "a steadily increasing threat to regional peace and stability," a statement said.
Monday's briefing comes a day after at least 82 people were killed in violence nationwide in Syria – among them 40 civilians – according to figures supplied by Britain-based watchdog the Syrian Observatory for Human Rights.
Three children from one family were among five people killed in a strike by regime warplanes on Monday on the northern city of Aleppo, the country's commercial hub that has been a focus for fighting since mid-July.
"Three children from the same family were killed when their building collapsed in Maadi district, which is located in the Old City of Aleppo, 600 metres (yards) from the citadel," the Observatory's Rami Abdel Rahman told AFP.
"There are still people buried under the rubble."
Battles raged overnight in Aleppo's western districts of Jamiliyeh, Bustan al-Qasr, Furqan and in Zabdiyeh, while the army shelled rebel positions in Marjeh, Tariq al-Bab and Zabdiyeh, the Observatory said.
In Damascus, pre-dawn battles erupted in the eastern neighbourhood of Qaboon, said the watchdog, while northwest of the city, a large explosion rocked Qudsaya suburb after midnight.
The northeast suburb of Douma and farmland between Douma and nearby Harasta were also shelled overnight.
On Sunday, regime aircraft hammered rebel strongholds as rebels said they now control most of Syria and have moved their command centre from Turkey to "liberated areas" inside the country.
The air attacks focused on Homs province, Deir Ezzor in the east and areas of Damascus.
In Aleppo, rebels destroyed two fighter planes on the ground in Orm, a rebel commander told AFP.
Residents in the village of Bianoun, north of Aleppo, told AFP that aircraft also hit a rebel house where a meeting was under way, destroying it and killing everyone inside. The report could not be independently verified.
Colonel Ahmad Abdul Wahab of the Free Syrian Army said the regime's aerial superiority was the only thing preventing the FSA from seizing the capital.
"We control most of the country. In most regions, the soldiers are prisoners of their barracks. They go out very little and we can move freely everywhere, except Damascus," Abdul Wahab told AFP.
On Saturday, the FSA said the next step would be to "liberate" Damascus.
Nearly 80 percent of towns and villages along the Turkish border are outside the control of the authorities in Damascus, according to the Observatory.
In the capital, 20 government-tolerated opposition parties met on Sunday to discuss a solution to the crisis in the presence of the ambassadors of Russia and Iran, staunch allies of Assad's government.
Raja al-Nasser of the National Coordination Committee for Democratic Change called at the meeting for an end to the "barbaric bombing" to move toward a political process that would "put an end to the current regime."
According to the Observatory, at least 29,000 people have been killed since the revolt against Assad's rule erupted last year. The United Nations puts the toll at more than 20,000.
Because of international divisions over the 18-month-old conflict, the UN is holding no formal meeting on Syria at this week's General Assembly.
But US President Barack Obama and Western leaders are expected to call for action in their speeches. Obama is one of the first speakers on Tuesday after Ban formally opens the annual gathering of world leaders.
Diplomatic wounds over Syria are not close to healing, however. Neither Russia nor China, which have three times vetoed Security Council resolutions on Syria, will be represented by a senior leader in New York.
Assad is expected to send his foreign minister, Walid Muallem.
"Everyone will be thinking about Syria, talking about Syria, but there will be no decision and no major progress," said one senior UN diplomat, speaking on condition of anonymity.