But the Syrian government and opposition groups are not meeting directly.
Instead, a U.N. special envoy is trying to find common ground between the parties before more people are killed.
Special envoy Staffan de Mistura said he met Monday with the main Syrian opposition group, called the High Negotiations Committee. They demanded not just a political solution, he said, but also "facts on the ground, in reduction of the violence, in the fact of the detainees, in the fact of the besieged areas."
De Mistura said a cease-fire in Syria is a top goal, but his immediate objectives are to keep the talks going and obtain a list of Syrians detained by the government.
Previous talks have failed. If the Syrian government came through with a list of names, that would be a signal that "there is something different happening," he said.
He'll meet Tuesday with the Syrian government.
The opposition group said it's eager to make progress.
"We are here, we are ready to make this a success, we are ready to start negotiations," High Negotiations Committee spokesman Salim al-Muslat said before the meeting.
But the odds are formidable.
And the U.N.'s High Commissioner for Human Rights Zeid Ra'ad Al Hussein ruled out any prospect of an amnesty for the most serious crimes committed in the nearly 5-year-old civil war. "In the case of Syria, we are there to remind everyone that where there are allegations that reach the threshold of war crimes or crimes against humanity that amnesties are not permissible," he said.
"Clearly when looking most recently at the forced starvation of the people of Madaya, and there are 15 other besieged towns and cities, that this is not just a war crime but a crime against humanity if proven in court."
Two earlier rounds of peace talks have yielded no lasting ceasefire. Two other U.N. special envoys trying to forge peace in Syria have come and gone. And all the while, the conflict that has claimed more than 300,000 lives rages on.
De Mistura and Ramzy Ezzeldin Ramzy, the U.N. deputy special envoy, started their work Saturday night. De Mistura went to the hotel where the negotiations committee was staying after he flew in. The short informal meeting addressed issues relating to the talks, said a statement.
What U.N. Security Council resolution says
De Mistura is trying to get everyone on board with a U.N. Security Council resolution
adopted last month. According to the resolution, the Security Council calls for:
• An immediate stop in violence against civilians.
• A Syrian-led political process facilitated by the United Nations that would establish "credible, inclusive, and nonsectarian governance" within six months and would schedule the drafting of a new constitution.
• Free and fair elections, in accordance to the new constitution, to be held within 18 months.
• An inclusive transitional governing body formed with mutual consent.
• Safe and unhindered access for humanitarian aid groups to reach Syrians in need.
But the crisis won't be easy to solve. Syrian President Bashar al-Assad
has offered no indication he will step aside. And opposition members continue demanding an end of 44 years of Assad family rule.
The current talks are the first time in two years that the warring sides in Syria are meeting in an effort to end the civil war. The goal is a ceasefire agreement among all factions in Syria, except for ISIS
and al Qaeda-affiliated al Nusra Front -- two terror groups that have taken advantage of Syria's instability and have gained traction in the country.
Opposition lays out demands
This round of peace talks was initially set to begin last week but was held up because of discussions about who should represent the opposition, de Mistura said.
The U.N. special envoy has said his mandate is to involve "the broadest possible spectrum of the opposition." The High Negotiations Committee includes members ranging from a former prime minister to hard-core Islamist groups.
Opposition members have listed their own demands for the regime. They say they want an end to aerial bombardments; the release of prisoners, particularly women and children; and humanitarian access to beleaguered areas.
"It's important to us to see that food goes to our children who are starving to death," Muslat said.
Syrian regime responds
Bashar Jaafari, the Syrian government's lead negotiator and ambassador to the United Nations, said the regime would consider the opposition group's demands.
"Absolutely, because this is part of the agenda that we agreed upon, and that will be one of the very important topics that we will discuss amongst ourselves as Syrian citizens," Jaafari said Sunday.
He added that there would be no preconditions -- indicating the regime would not do what the opposition asks before the talks are settled.
Jaafari also said it's difficult to discern who may be terrorists among the opposition.
"We are not holding talks with individuals. We are not having talks with terrorists," he said.
"We have a very big gap as to identifying who (are) terrorists and who is not, who is the opposition, and who is not."
Russia is also planning to hold talks with U.N. envoy de Mistura and the U.S. delegation on Monday in Geneva, Russian Deputy Foreign Minister Gennady Gatilov told state news agency RIA Novosti.
More starvation deaths
As parties work toward an agreement, many Syrians are on the brink of starvation.
The United Nations says 400,000 Syrians badly need food aid.
At least 16 people have died of starvation in the city of Madaya in recent weeks, said the aid group Medecins Sans Frontieres, also known as Doctors Without Borders. Those deaths came even after the city received three rare aid convoys of food and medical supplies.
In addition to the starvation deaths, there are 320 cases of malnutrition, the group said
Madaya is a rebel-held city that has been choked off by government blockades and landmines.
Opposition activists have accused Hezbollah, the Lebanese militant and political group, of helping the Syrian government's siege of Madaya. But Hezbollah, in turn, has blamed rebel groups for preventing aid convoys from reaching the town.