Sources said representatives of the Transitional Federal Government (TFG) and a faction of the Eritrea-based Alliance for the Re-liberation of Somalia (ARS), led by Sheikh Sharif Sheikh Ahmed, began the latest talks on 22 November.
The most important points under discussion were the agreement on a Justice and Reconciliation Commission and power-sharing.
Ibrahim Habeb Nur, Minister of Public Works and Housing, a member of the government delegation, told IRIN the two sides agreed on the need to set up "a commission that deals with crimes committed".
He said they had also set up a six-member committee to devise modalities of power-sharing. "The committee on power-sharing is now meeting and is expected to present its report soon."
A power-sharing deal is expected to lead to a government of national unity, according to a local journalist.
Neither the armed wing of the Islamic Courts, the Al-Shabab group, nor the Asmara faction of the ARS, led by Sheikh Hassan Dahir, was involved in the Djibouti talks.
An observer at the talks, who requested anonymity, told IRIN that the negotiations were going well but without the involvement of the armed groups waging the war inside the country, implementing any agreement "is almost impossible".
"Neither the TFG nor the ARS-Djibouti can stop the fighting in Mogadishu. They have to find a way to convince the armed groups," he added.
The violence erupted as a deadline for the withdrawal of Ethiopian troops from designated areas of Mogadishu expired on 21 November.
Ahmed Abdisalam, Deputy Prime Minister and Minister of Information, told IRIN the fighting was "a deliberate attempt" to undermine the peace process. "There are groups that do not want peace and will do whatever it takes to undermine the whole process."
The withdrawal, he added, was under way and would be completed. "The 21 November date is only a starting point. No one expects it to happen in one day. The whole process was supposed to take 30 days."
Abdisalam, who was on his way to Djibouti, said talks were going well and the two sides were getting closer. Appealing to those outside the talks to come aboard, he said: "Eighteen years of fighting did not resolve our problems, why not give the talks a chance."
But a spokesman for the Islamic Courts accused the Ethiopians of refusing to leave. "The same day they [Ethiopian troops] were supposed to withdraw, they try and expand the areas of their control," said Sheikh Abdirihin Isse Adow.
"All we did is defend our people," he added. "From where we stand they don't look like they are going anywhere, and so long as they are here we will continue our struggle to liberate our country."
According to sources in Mogadishu, at least 40 people died over the weekend and 70 were injured.
"The weekend fighting was very intense and widespread," said a local journalist. "By the measure of Mogadishu, this was a bad one."
A civil society activist told IRIN that both sides seemed to be using the deadline as a reason for the clashes. "Someone needs to break the logjam and spare the population," he said.
Medical staff told IRIN that among the dead were eight children. "Six were killed while playing football in Yaqshid district. The other two were killed when a shell landed on their Koranic school," he said.
Ethiopian forces entered Somalia in December 2006 and ousted the Union of Islamic Courts, which controlled much of southern and central Somalia.
Fighting between them, Somali forces and insurgents began in early 2007, forcing an estimated one million Somalis out of their homes. According to the UN, 2.6 million Somalis need assistance. That number is expected to reach 3.5 million by the end of the year.
[Listen to IRIN's daily news podcast in Somali]