Congolese soldiers have been conducting operations against rebels in the M23 movement
The proposed force would tackle militia groups in the eastern DR Congo.
DR Congo and Rwanda often accuse each other of backing rival rebel groups, and have gone to war in the past.
Recent rebel advances in eastern Congo have led to thousands of displaced civilians.
On Sunday, Mr Kagame and Congolese President Joseph Kabila held a one-to-one meeting at the headquarters of the African Union in Addis Ababa in Ethiopia, aides said.M23 rebellion
According to a declaration seen by Reuters news agency, they agreed to "work with the AU and the UN for an immediate establishment of a neutral international force to eradicate" armed groups in eastern DR Congo.
The also reportedly says that no support should be given to "any negative force" to "destabilise the region and eastern Congo in particular".
Mr Kagame said that the exact details of the force - including its size, mandate, nationality and deployment details - had yet to be defined.
The conflict, which has killed and displaced million of civilians over nearly two decades, has its roots in Tutsi-Hutu enmities dating back to Rwanda's 1994 genocide.
The UN already has a peacekeeping mission of more than 17,000 in DR Congo but has often struggled to stem fighting in the vast country.
AU Peace and Security Commissioner Ramtane Lamamra said that changing the mandate of the UN peacekeeping mission there "was one scenario", AFP reports.
In June, a UN report accused Rwanda of supporting Congolese rebels, among whom are a Tutsi-led group known as the M23 rebellion.
The group takes its name from a 2009 peace accord which the rebels say was violated by Kinshasa.
The group has been joined by hundreds of Congolese army defectors who abandoned their posts in support of fugitive Congolese General Bosco Ntaganda, wanted by the International Criminal Court on war crimes charges.