Rebels in the Democratic Republic of Congo loyal to General Laurent Nkunda have called for peace talks with the government to resolve the crisis.
Gen Nkunda says he is protecting DR Congo's Tutsi community
The rebels have pushed back army forces, regaining the territory lost in last week's government offensive.
Up to now President Joseph Kabila has ruled out negotiations with Gen Nkunda.
Meanwhile, UN chief Ban Ki-moon has called on the rebels to lay down their weapons and for both sides to protect the civilians caught up in fighting.
Gen Nkunda claims to defend DR Congo's Tutsi population against Rwandan Hutu rebels - both Interahamwe militia and former Rwandan armed forces - who have lived in eastern DR Congo since the Rwandan genocide in 1994.
The government had repeatedly warned him to stop his rebellion and integrate his men into the army.
The army has deployed more than 20,000 soldiers in the region to try to defeat the rebel force which is thought to number 6,000-8,000 men.
Rebel spokesman Rene Abandi said they were calling for negotiations because they had the upper hand and wanted the government to listen to its solution to the problems of eastern DR Congo.
"We are calling for a political solution - to end discrimination against some communities to solve the problem of the Interahamwe and to organise a modern army," he told the BBC's Network Africa programme.
"We are asking for negotiations because they thought at the beginning that we were not strong, but now that we have won we can explain our vision to solve political problems."
"We believe that the solution to the problem is political and not military, even though the situation on the ground is currently in our favour."
Mr Abandi denied accusations that the rebels are forcibly recruiting child soldiers.
Some 400,000 people have been displaced in fighting over the last few months.
Mr Ban Ki-moon expressed his "deep concern" for the displaced civilians.
The UN Secretary-General's press secretary said Mr Ban was "particularly troubled by reports of massive displacement and mistreatment of the population."
The UN High Commissioner for Refugees, Antonio Guterres, has begun a five-day visit to the region to assess the situation.
The rebels have continued to advance on the town of Sake, some 30km north-west of Goma, pushing back the government forces.
The BBC's Arnaud Zajtman who is not far from the frontline says UN peacekeepers have set up positions in the surrounding hills.