(CNN) -- Syria's warring sides met face-to-face again Tuesday, but little progress was made as yet more bitter accusations were exchanged between both sides.
U.N. envoy Lakhdar Brahimi moderated the meeting in Geneva, Switzerland, after a first round of talks just a few weeks ago failed to make significant progress.
But neither is budging from their negotiating positions.
Speaking to reporters, Monzer Akbik, a spokesman for the opposition Syrian National Coalition, said his delegation had submitted an initiative for a political transition to end a humanitarian crisis and accused the government of not listening to the demands of the people.
"We don't have barrel bombs, we are not the one killing our people," he said.
Meanwhile, Syrian state television flashed an urgent banner quoting Syrian Ambassador to the United Nations Bashar Jaafari as saying the government delegation would not participate in further negotiations unless the opposition commits to "fighting terrorism" in Syria.
"There can be no talk of a true political process without stopping violence, terrorism and foreign interference," he was quoted as saying.
The Geneva II peace conference, which had its first session 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.
Brahimi said then that some "common ground" had been reached.
Both sides had met Brahimi separately Monday, and at the time, the opposition delegation said each side would meet with him separately until the U.N. envoy decided there was common ground for joint discussions.
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.
The opposition 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.
Evacuations from besieged city
As the peace conference gets under way, the Syrian government and opposition are discussing whether to extend a truce in the besieged city of Homs by another three days, the United Nations refugee agency said Tuesday.
More than 1,100 civilians have been given safe passage out of the Old City portion of Homs since a first "humanitarian pause" deal was put in place Friday, the agency said.
Syria's Red Crescent tweeted that about 300 people were taken to safety early Monday. Evacuations continued Tuesday, according to the United Nations.
At least 500 children were among civilians evacuated from the besieged old city, according to UNICEF. Its colleagues said the children who came out looked terrified, frail and emaciated.
"Mothers were anxious, and many were crying. All they wanted was for their children to reach safety," UNICEF said in a written statement.
Of those evacuated, 336 men between the ages of 15 and 55 were being questioned by Syrian authorities in an abandoned school, the United Nations said.
Parts of Homs have been under siege since June 2012.
The U.N.-brokered truce has been violated several times. 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.
Elsewhere, in the northern Syrian city of Aleppo, government military helicopters dropped barrel bombs on parts of the city, and the Syrian military shelled opposition neighborhoods there, killing at least 30 people and wounding tens of others, the opposition Aleppo Media Center said.
Barrel bombs are drums packed with explosives and shrapnel. Aleppo and its surrounding areas are a key battleground in Syria's nearly 3-year-old civil war.
The Syrian conflict has claimed more than 100,000 lives and displaced millions more since it began in 2011, creating a major humanitarian crisis within the country and for its neighbors.