The CNDP controlled large parts of eastern Congo with the tacit support of Kagame, and the two were reputed to be close strategic allies.
Circumstances apparently shifted after Nkunda's forces were accused of committing war crimes, and Kagame - under pressure for the West - struck a deal with Joseph Kabila, the DR Congo president, last month.
"In working together, we had to confront and deal with two problems, one is the FDLR [Hutu fighters] problem - that is genocidal forces in the DRC that had to be dealt with," Kagame said.
"And secondly, we had to work together again to deal with the problem of the eastern Congo conflict which is otherwise internal to the Congo, but has links to Rwanda."
Protracted fighting in eastern Congo between Nkunda's forces, Hutu fighters, and at times the DR Congo army, has displaced around two million people - and the violence has threatened to spill over the border.
The Rwandan army has crossed the border into the Democratic Republic of Congo to disarm the Hutu fighters that fled there after the Rwandan genocide in 1994.
Sporadic clashes between the Rwandan army and the FDLR have gone on for a week, Laforge Fils, a rebel spokesman, told the AFP news agency on Thursday.
Thousands more troops are expected to join the operation.
According to Kagame, both countries are now working to improve ties.
"First, we've been working together to normalise our relations. Secondly, to build on that and confront the challenges that are there in terms of the crisis that has been there for very long, and therefore deal with the problems that underlie this conflict," he said.
Nkunda, currently in Rwandan custody, is likely to be extradited to Congo to stand trial. Kagame said he hoped that would happen next month.