The African Union in February selected Rwanda to replace South Africa on the Security Council for a two-year term starting on January 1. Since Rwanda is the only candidate for the seat, its election by the UN General Assembly in September is virtually assured.
Earlier this month, HRW accused Rwanda's military of providing weapons and refuge to ex-warlord Bosco Ntaganda, whose fighters have launched a new rebellion in neighbouring eastern Congo.
The ICC has sought his arrest for war crimes since 2006, though Congo's government had allowed him to operate freely as a general in its army, only recently vowing to capture him.
Rwanda's Foreign Minister Louise Mushikiwabo has dismissed HRW's claims as "categorically false and dangerous".
Implicated in crimes against children
HRW's UN director, Philippe Bolopion, said on Monday if Rwanda wants to be a responsible Security Council member it should cut off all support for Ntaganda, actively seek to arrest him, and surrender him to the ICC.
"By allowing its territory to be used to protect and arm an ICC-indicted war criminal, Rwanda is making a mockery of the decisions of the same Security Council it is slated to join next year," Bolopion told AP.
"Bosco Ntaganda is not only implicated in horrendous crimes against civilians including children, he is also undermining everything the Security Council has tried to achieve at great expense in the region for the last decade."
Rwanda's UN Ambassador Eugene-Richard Gasana said on Monday that Rwanda was the unanimous choice of the African Union for a council seat and "all member states know very well ... that Rwanda today is among the top six contributors in the world of UN peacekeepers".
"So it's kind of surreal to think that that very country which is critically involved in the peace and security around the world - on the one hand - would on the other hand think that we would be troublemakers," Gasan told AP. "We can't shoot ourselves in the foot."
He said Mushikiwabo is currently in Congo to discuss the upsurge in fighting in the east and to support efforts to bring peace and security to the region.
Eastern Congo has been engulfed in fighting since the 1994 Rwanda genocide, in which at least 500 000 Tutsis and moderate Hutus were slaughtered by Hutu militias before a Tutsi-led rebel army took power in Rwanda.
More than 1 million Rwandan Hutus fled across the border into Congo, and Rwanda has invaded Congo to take action against Hutu militias there.
Ntaganda, who is a Tutsi, was a feared warlord until he joined the Congolese army in 2009 as a general following a peace deal that paved the way for him and his men to be integrated into the military.
He was allowed to live freely in the provincial capital of Goma, despite the ICC arrest warrant, but in late April the peace deal fell apart and Ntaganda and his troops defected from the army.