UN Syria envoy Staffan de Mistura voiced "horror and outrage" at the attacks claimed by the Islamic State group that killed around 35 people in the Belgian capital Tuesday.
"The tragedy in Brussels ... reminds us that ... we have no time to lose," UN Syria envoy Staffan de Mistura told reporters in Geneva.
"We need to extinguish the fire of war in Syria," he said, insisting that "to fight terrorism, the best formula is to find a solution for political transition in Syria."
The main opposition umbrella group, the High Negotiations Committee (HNC) also stressed the need to rapidly end the five-year conflict, which has killed more than 270,000 people and displaced millions.
HNC spokeswoman Bassma Kodmani said the UN-brokered Syrian peace talks were "more vital than ever".
"The Geneva process is today fundamental to reestablishing the global political order and avoiding the chaos that fanatics are threatening us with here in Europe and there in the Middle East," she said in a statement.
- Snail's pace -
But despite the calls to speed up the process, the Geneva talks, which are in their second week, remain indirect and continue to move at a snail's pace.
Conceding that progress remains slow, de Mistura has stressed the importance of getting the opposing sides to reach a basic understanding on how to advance to a second round of talks, tentatively scheduled for next month.
The envoy, who has been shuttling between the two sides, said Tuesday he is eager to make progress before the negotiations pause on Thursday, telling reporters: "We are all working hard on getting a common understanding."
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But the talks continue to stumble on the fate of Syrian President Bashar al-Assad, with the regime's lead negotiator in Geneva, Bashar al-Jaafari on Monday reiterating that discussing the issue was "excluded."
Hisham Marwa, who serves as a consultant in the HNC delegation, meanwhile told AFP Tuesday that any talk of leaving Assad in power is "absolutely unacceptable".
Assad's fate has been a key obstacle in the latest talks aimed at ending Syria's devastating five-year war, which has killed more than 270,000 people and displaced millions.
France-based Middle-East expert Agnes Levallois told AFP the regime was dragging its feet in the talks, "because when real negotiations begin, it will be the beginning of the end."
She said its only hope was to stall until "de Mistura throws in the towel just like his predecessors," Kofi Annan in 2012 and Lakhdar Brahimi in 2014.
- 'Strong expectations' for Moscow meet -
But de Mistura appeared far from defeated, hailing a more positive atmosphere than during a previous aborted round, largely helped by a fragile ceasefire declared on February 27.
On Tuesday, he said there was "some level of mutual respect", and stressed "we have not had walk-outs or slamming of doors."
The partial ceasefire has raised hopes for an end to the violence, which were further fuelled when Russia -- a key backer of Assad -- announced last week it would withdraw most of its troops from Syria.
De Mistura also voiced hope that a meeting between US Secretary of State John Kerry with his Russian counterpart Sergei Lavrov in Moscow on Wednesday could provide momentum to the peace drive.
"They have been proving in the past, and I hope they will prove it in the future, that when they do have a common understanding it helps enormously the process," he said.
The envoy said he had "a strong expectation that the talks in Moscow will be productive."