"According to our sources, at least 15 people were killed in the town of Faradje, which suffered looting and destruction of homes," Monuc said in a statement.
The UN mission said it had deployed around 100 Congolese soldiers in Faradje on Friday to protect civilians. Uganda was also sending more forces to the area.
Uganda, Congo and South Sudan are waging a joint battle against the LRA in Congo.
Chris Magezi, the spokesman of the military operation, said three more people were killed on a road in south Sudan and five bodies found along the Congo-Sudan border.
Kony not found
The joint military offensive was launched after LRA's leader Joseph Kony repeatedly refused to sign a peace agreement with the Ugandan government.
So far, attempts to locate Kony have failed.
Magezi said Ugandan forces believed Kony's fighters were moving towards the Central African Republic, which borders Congo and Sudan.
On Monday, an LRA spokesman said Kony and his top commanders had survived bomb raids on their bases. He said Kony was calling for peace talks to be relaunched with a new mediator.
Kony and two of his deputies have been indicted by the International Criminal Court in The Hague for war crimes allegedly committed during a two-decade war that has killed thousands of people and displaced about two million more.
The LRA is infamous for kidnapping women and using children as fighters.