Government forces and rebels clashed on Saturday in the Rockero area of North Darfur state, according to the mission, which was unable to estimate the number of casualties from the violence.
In Abu Surug in South Darfur state, the Local Defence Force fought about 120 armed men, believed to be from an Arab militia, also on Saturday, UNMIS said.
More internally displaced persons (IDPs) have been arriving at Al Salam camp in South Darfur in the past few days, driving by recent attacks on their villages by armed Arab militiamen.
The weekend clashes are the latest to strike Darfur, the arid and impoverished region that has become the scene of the world's worst humanitarian crisis since rebel groups took up arms in 2003 against Government forces, which were subsequently backed by the notorious Janjaweed militias.
More than 200,000 people have been killed and at least 2 million others have been displaced, while the destruction of villages has also been widespread.
On Friday, the Secretary-General's Special Envoy for Darfur, Jan Eliasson, said formal political negotiations to resolve the conflict could begin soon, with many of the warring parties indicating they are ready to sit down and talk.
He told reporters that the pre-negotiations phase has almost concluded, with the convergence of several parallel efforts by Sudan's neighbours and the UN to end the fighting.
"We have the beginning now of a credible political process," Mr. Eliasson said, adding that "we are now at the stage where we will practically prepare for the negotiations."
One of the biggest obstacles is the number of rebel movements in Darfur, which have grown because the movements have splintered into factions since 2003. At least nine distinct groups are now fighting the Government.
Meanwhile, UNMIS reported that a group of Lord's Resistance Army (LRA) members have recently abducted four civilians at a village in Central Equatoria state in southern Sudan.
The LRA, which has been waging a notorious insurgency in northern Uganda since 1986, has a record of abducting children and then using them as soldiers or porters, while subjecting some to torture and allocating many girls to senior officers in a form of institutional rape.
UNMIS said it learned of the recent abductions from the Sudan People's Liberation Army (SPLA), the former rebel group which is now involved in the Government of southern Sudan as part of a power-sharing deal after the end of the north-south civil war in early 2005.
A team of negotiators led by the Southern Sudanese Information Minister and an LRA Brigadier-General went to the area around Dimo, the village where the abductions occurred, on Saturday, to try to negotiate the release of the civilians.