This while Gulf Arab states urged a rapid political transition in the country.
Pope Benedict XVI meanwhile called in his traditional Christmas message for "an end to the bloodshed" and for "dialogue in the pursuit of a political solution" in Syria.
Brahimi, the UN-Arab League's special envoy to Syria, held talks at his Damascus hotel with a delegation of six people led by Hassan Abdel Azim, head of the National Coordination Committee for Democratic Change (NCCDC), an opposition group tolerated by the regime.
NCCDC chief Hassan Abdel Azim said after the talks that Brahimi would stay in Syria until Sunday "to try to implement an international consensus to end the crisis." His deputy Raja Nasser was more forthcoming.
"The only solution is a transitional government that holds all powers," Nasser told reporters, adding that Brahimi was to hold further meetings with government officials. "A political solution is the only solution, and this means the establishment of a new democratic regime instead of the current regime," he added.
The comments come in the wake of a report by a French daily of a supposed US-Russian initiative for a transition in Syria, which has caused rage among opponents who reject any compromise with the regime.
Le Figaro newspaper said a solution in the offing would involve keeping Assad in power until 2014 while preventing him from further renewing his mandate. The Local Coordination Committees, a grassroots network of anti-regime activists, blasted Brahimi and the international community for failing to stop the bloodshed.
On Monday alone, at least 126 people died in violence across Syria, according to the Syrian Observatory for Human Rights, adding to its figure of more than 44,000 people killed since an uprising against Assad erupted in March last year.
"Brahimi's arrival in Damascus to discuss a new political initiative to solve the crisis caused by the regime… has not put a stop… to massacres," the LCC said in a statement. "Regarding leaks about an initiative proposed by Brahimi, the LCC declares its rejection of any initiative that puts Syrians in a position where they are extorted and forced to choose between accepting unfair compromises, or the continuation of the regime's crimes against them," it added.
The opposition Muslim Brotherhood too dismissed any compromise that would leave Assad in power. "We hold the UN Security Council and all relevant international organisations fully responsible, now and in future, for all the crimes against humanity that Bashar al-Assad and his gangs have committed against the people of Syria," it said in a statement.
"We consider that giving Assad the opportunity to commit an endless string of crimes is tantamount to complicity in these crimes." Brahimi met with Assad on Monday, saying afterwards that they had "exchanged views on the many steps to be taken in the future" regarding the "always worrying" Syrian crisis. Assad had described his meeting with Brahimi as "friendly and constructive".
Syria's conflict broke out when a peaceful uprising against Assad morphed into a bloody insurgency after the regime unleashed a brutal campaign of repression against dissent. Despite efforts by Brahimi and his predecessor Kofi Annan to secure a truce, fighting has raged across Syria, with rebels and troops locked in a stalemate in flashpoints that has killed thousands and sent hundreds of thousands of civilians fleeing their homes.
As the violence has escalated, the international community has expressed increasing concern of the risk to the stability of the entire region. On Tuesday, representatives of the six oil-rich Gulf Cooperation Council states, meeting in Bahrain, urged a rapid political transition in Syria.
The GCC expressed "deep sadness over the continued shedding of blood by the regime and the destruction of cities and infrastructure, making political transition a demand which must be rapidly implemented."
The Pope in his Christmas message that touched on several other of the world's conflict zones, pleaded for a peaceful solution in Syria. "Once again I appeal for an end to the bloodshed, easier access for the relief of refugees and the displaced, and dialogue in the pursuit of a political solution to the conflict," he said. Sapa-AFP