Persistent fighting in the east of the mineral-rich DRC pits federal troops against rebels from the M23 group, which has captured swathes of territory.
The DRC, along with the United States and several European countries, has repeatedly accused Rwanda of backing the Tutsi-led rebels from M23, although Kigali denies the charge.
Tensions have soared and thousands have fled the battles into neighbouring states, including Rwanda.
In November, the UN said around 72,000 Congolese had crossed into Rwanda.
“There is one type of refugee that I think we are not going to accept,” Kagame said in reference to the Congolese refugees.
“We cannot keep hosting refugees for which later on we are held accountable in some way, or even insulted and abused about,” he told the Senate in the capital Kigali on Monday.
“This is not Rwanda’s problem. And we are going to ensure that everybody realises that it is not Rwanda’s problem,” he vowed.
“I am refusing that Rwanda should carry this burden,” he said.
Kigali has repeatedly blamed Kinshasa for the crisis and accused the international community of turning a blind eye to DR Congo’s alleged support for the Democratic Forces for the Liberation of Rwanda (FDLR), a mainly Rwandan Hutu rebel movement implicated in the genocide of Tutsis in 1994.
Kigali sees the FDLR as a threat which justifies incursions into the DRC.
Rwanda has also accused the DRC– where presidential elections are due next December – of using the conflict for political purposes as well as of “fabricating” a November massacre of at least 131 civilians.
A UN probe blamed the deaths on M23 rebels.
A tentative ceasefire and the deployment of Kenyan forces through the East African Community (EAC) have so far failed to halt the bloodshed.
The UK government has signed a deal with Rwanda to fly illegal arrivals there before their asylum claims are even considered.
If eventually granted refuge, they will remain in Rwanda rather than return to the UK.
