cnn — GENEVA, Switzerland (CNN) -- Syria's warring sides began a new round of peace talks Monday, days after a first session managed little beyond a pledge to evacuate civilians from the besieged city of Homs.
The Geneva II peace conference, which had its first session some 10 days ago, brought the Syrian government and opposition together for face-to-face negotiations for the first time since the conflict began nearly three years ago.
The first round of talks ended with no firm agreements and bitter statements from both sides.
However, United Nations envoy Lakhdar Brahimi said then that some "common ground" had been reached.
He met with the Syrian opposition in Geneva on Monday morning before separate talks with the government representatives.
According to a document obtained by CNN detailing the Syrian opposition's talking points for its meeting with Brahimi, the delegation reiterated its call for the formation of a transitional government body and asked for a discussion of an end to the government shelling of cities such as Aleppo, which has been subject to punishing air raids.
The opposition delegation said each side would meet with Brahimi separately until the U.N. envoy decided there was common ground for joint discussions.
The government delegation meanwhile decried violence in Syria that it said was carried out by "terrorist armed groups."
"The Syrian delegation to this conference in insisting on putting an end to terrorism," Syrian Deputy Foreign Minister Faisal al-Mikdad told reporters in Geneva.
Under fire in Homs
The new round of talks comes after hundreds of people were evacuated from Homs. More than 600 people -- women, children, the sick and the elderly -- were convoyed out of the restive city on Sunday after gunfire interrupted a U.N.-brokered humanitarian pause.
Vehicles from the Red Crescent and United Nations had a difficult time entering the city over the weekend as they were targeted by gunfire and explosives.
But workers managed to deliver some aid to the thousands of people in the besieged section of the city known as the Old City of Homs, where rebels battle government troops and each other.
Homs is just one of 40 besieged communities in Syria, according to the U.N.'s World Food Programme, which says about a quarter of a million people have been cut off from humanitarian aid for months.
"We acknowledge this is a step toward easing the siege," Ertharin Cousin, WFP executive director, said in a written statement.
"But one-off convoys into besieged areas offer only a minimum of relief. WFP demands continuous and sustainable access to provide food and to monitor and assess needs."
The conflict has claimed more than 100,000 lives and displaced millions more since it began in 2011, creating a major humanitarian crisis within Syria and for its neighbors
At the end of the last talks, the two warring sides appeared to be a long way from reaching any compromise.
The government insists that the talks focus on fighting "terrorism" -- its description of the uprising -- but the opposition says the priority should be the removal of President Bashar al-Assad.
It has insisted that the government commit in writing to the 2012 Geneva I communique, which called for the formation of a transitional government.
Al-Assad's government has ruled out any transfer of power.
Call for a UN resolution
As the talks resume, French Foreign Minister Laurent Fabius said France and other countries would present a resolution at the United Nations calling for greater access for humanitarian aid.
"We are asking for stronger action as far as the humanitarian side is concerned, that medicines and food supplies are handed out in cities," he told French radio RTL.
"It is absolutely scandalous that there have been discussions for quite a while and that people are still being starved every day, and so along with a number of other countries, we will present a resolution at the U.N. along those lines."
A French Foreign Ministry spokesman said it was too early to say when such a resolution would be presented at the U.N. Security Council.
British Foreign Secretary William Hague echoed Fabius' comments.
"Humanitarian access is a vitally important issue in Syria, and the UK will be pushing this issue this week at the UNSC, and proposing that the Security Council takes a firmer position and passes a resolution on this in order to require humanitarian access in Syria," he told reporters in Brussels.
-- CNN's Bastien Invaurralde contributed to this report
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