In a state address, Kagame said "the whole world" was putting the blame for the crisis on Rwanda but he says it was DRC's President Felix Tshisekedi seeking to gain from the unrest - with elections on the horizon.
DRC will hold its next presidential poll in December 2023.
"This problem can be resolved if one country headed for elections next year does not try to create grounds for an emergency so that elections do not take place," Kagame said at a swearing-in ceremony for new cabinet members.
"If he is trying to find another way of having the next elections postponed, then I would rather he used other excuses, and not us."
Fighting in eastern Congo between government forces and M23 rebels has heightened tensions with neighbouring Rwanda, which the DRC accuses of abetting the militia -- a charge Kigali denies.
Talks between the two countries in Angola last week did result in a ceasefire that paused the fighting, and several days later the truce appears to be holding.
Another round of talks with armed groups continued in Kenya on Wednesday, without the M23 present.
Uhuru Kenyatta, the former Kenyan president who is facilitating the talks, said foreign rebel groups operating in Congo "should get out" or face DRC and East African troops.
"Already they have been given notice: DRC will not be a center for fighting by other countries," Kenyatta said.
DRC and Rwanda have accused each other of backing rebel groups and the resurgence of M23 has pushed diplomatic tensions to fresh highs.
Under the ceasefire that came into force on November 25, M23 fighters were to withdraw from "occupied zones" in eastern Congo, failing which an East African regional force would intervene.
The M23 is among scores of armed groups that have turned eastern DRC into one of Africa's most violent regions.