The delegation of the High Negotiations Committee (HNC) said during the peace talks in Geneva they held "very positive" discussions with UN Special Envoy Staffan de Mistura, notably on the humanitarian situation.
The HNC said earlier in the day it would not enter political negotiations with Bashar al Assad's regime until there were concrete measures in place that would alleviate the humanitarian situation on the ground.
"Today's meeting was very positive with Mr de Mistura," HNC spokesman said and added, "Things are encouraging and positive concerning humanitarian issues. There will be another meeting tomorrow."
HNC is seeking a halt to attacks on civilian areas, the release of detainees and a lifting of blockades. The measures were mentioned in a UN Security Council resolution approved last month that endorsed the peace process for Syria.
But Riad Hijab, the leading figure in the HNC, was not among the group that arrived in Geneva.
The HNC, which brings together representatives of the mainstream political opposition and rebel groups, said in an online statement that without the United Nations (UN) and international pressure on the Syrian regime there would be no justification for the main Saudi-backed opposition group to remain in Geneva.
"In view of the regime and its allies' insistence in violating the rights of the Syrian people, then the presence of the HNC delegation in Geneva would not have justification and the HNC could pull its negotiating team," Hijab said from the Saudi capital Riyadh.
Senior Syrian opposition negotiator Mohamed Alloush representing Jaish al Islam, a major rebel group, said on Sunday he was heading to Geneva to join his delegation and prove that Syrian authorities did not want a political settlement.
Alloush said "the regime has not implemented any measure of the goodwill steps" which the Saudi-backed main opposition group was demanding, such as halting bombardment and allowing humanitarian aid convoys into besieged rebel-held area.
"It's necessary for me to come to Geneva to show the world who is the terrorist who destroyed the country and displaced its people in documents and figures," he said.
DAESH suicide attack in Damascus
While the Geneva talks are ongoing, twin suicide blasts on Sunday rocked the Syrian capital Damascus, where sixty people were killed.
US Secretary of State John Kerry appealed on Sunday to both sides to continue Syrian peace talks in Geneva despite the attack claimed by DAESH terrorists.
Kerry said the conflict could easily engulf the Middle East if no negotiated settlement was achieved. He also called for immediate steps to increase food aid and other humanitarian assistance to Syrians.
"In the end there is no military solution to the conflict," Kerry said in a televised statement.
The UN said on Sunday that the Syrian town of Mouadamiya is under siege by Syrian regime forces, adding 45,000 to the number of people it says are cut off from humanitarian aid and medical help in Syria.
Regime has already attracted global criticism for its siege of Madaya, where dozens have starved to death.
Mouadamiya, on the southwestern edge of Damascus, has been under the control of opposition armed groups since mid-2012. Syrian regime forces surrounded it in 2013 but began allowing aid access in mid-2014 under a local deal.
However, regime forces closed the only entry point on Dec. 26 last year, after allowing 50-100 government employees to leave. Other civilians were not warned of the closure, said the UN.
"Due to increased closures imposed on the town in December 2015, the UN re-classified (Mouadamiya) as 'besieged' as of 27 January 2016," it said in a statement, adding that the town continued to be subject to sporadic shelling.
The UN said there were 486,700 people under siege in Syria, in areas controlled by the regime, DAESH and other armed groups, among about 4.6 million who are hard to reach with humanitarian aid.
The United Nations is aiming for six months of talks, first on a ceasefire, then working toward a political settlement to the civil war that has killed over 250,000 people, driven more than 10 million from their homes and drawn in global powers.