Aleppo, Syria's second city, saw fierce clashes between regime forces and rebels near an air force intelligence headquarters that the opposition tried to seize in a spectacular attack on Wednesday.
The attack, which began with a powerful explosives blast in a tunnel dug near the building, left at least 20 members of regime security forces and 14 rebels dead.
A Syrian military source told AFP the army had on Thursday launched an attack "against (rebel) gunmen positions" in the area, "killing and wounding many of them".
Regime forces also struck rebel-held territory in the east of the city, killing at least 22 civilians, including three children, in a single barrel bomb attack, said the Syrian Observatory for Human Rights, a monitoring group.
Aleppo has been hit by significant violence this week after the opposition rejected a UN plan for a temporary ceasefire in the divided and devastated city, once Syria's main commercial hub.
A UN delegation was in the city to push a plan for a temporary "freeze" of fighting in Aleppo which was rejected by the opposition on Sunday -- part of a range of efforts to resolve a conflict that has left more than 220,000 dead since March 2011.
- Opposition seeks 'common ground' -
Speaking to AFP in Paris, opposition National Coalition chief Khaled Khoja said a "new strategy" was needed and that while Assad's overthrow was still the final aim, it was not necessary for the start of a process to end Syria's conflict.
"We insist on the goal of toppling Assad and the security services... It is not necessary to have these conditions at the beginning of the process, but it is... necessary to end the process with a new regime and a new free Syria," he said.
Khoja also softened the coalition's previous refusal to work with Damascus-tolerated opposition groups, saying he wants "a common ground" with other dissidents and to "establish a new framework for the Syrian opposition."
The country's main domestic opposition group, the National Coordination Committee for Democratic Change (NCCDC), said Khoja's comments marked a welcome change.
"Any statement calling for the unification of the opposition is certainly positive, but concrete actions and effective positions are more important," NCCDC spokesman Monzer Khaddam said.
He also praised the Coalition for being prepared to drop its pre-condition for Assad to step down, saying the issue had been raised in joint opposition talks in Paris two weeks ago.
"We tried in Paris to convince them that all pre-conditions in no way help in finding a political solution in Syria," Khaddam said.
- Dashed ceasefire hopes -
Moscow meanwhile said it would host talks between representatives of Assad's regime and opposition figures in April, three months after a meeting between the parties ended without any concrete results.
In Saudi Arabia to meet with Gulf allies, Kerry upped pressure on Assad to negotiate, saying he had "lost any semblance of legitimacy" and raising the possibility of military pressure.
"Ultimately a combination of diplomacy and pressure will be needed to bring about a political transition. Military pressure particularly may be necessary given President Assad's reluctance to negotiate seriously," Kerry said in Riyadh.
The violence this week in Aleppo has dampened hopes of a ceasefire in the city, where UN envoy to the Syrian conflict Staffan de Mistura has been seeking a halt to fighting as a first step towards humanitarian aid deliveries in the area and a broader political deal.
Samir Nashar, a member of the National Coalition who is in contact with groups who attacked the regime building, said Wednesday's assault "sends a clear message to the regime and to De Mistura" that the rebels reject his initiative.
"De Mistura is at an impasse and is facing a dead end," Nashar told AFP. "De Mistura's initiative does not address even the minimum of rebel demands."
The Syrian Observatory for Human Rights said "a number of Al-Nusra Front leaders were killed" in an attack as they gathered for a meeting in the northwestern province of Idlib, but was unable to say if its chief, Abu Mohamed al-Jolani, was among them.
Observatory director Rami Abdel Rahman told AFP it was "not clear if the attack was carried out by the coalition or the regime".
Pentagon spokesman Colonel Steve Warren said he could not confirm the reports, but added: "Neither the US or the coalition have conducted airstrikes near that location in recent days."