Kagame said yesterday, the decision would only play into the hands of other rebels made up of remnants of Hutu extremists who carried out the 1994 Rwandan genocide.
"It benefits those enemies of our country who seek to destroy what we are trying to build," Kagame said in a speech to parliament.
The United Nations accuses Rwanda of backing the M23 rebels in neighbouring eastern DR Congo, a charge the country has adamantly denied.
But Kagame said the sanctions "benefit the people that throw grenades here in Kigali and killed our children", referring to recent attacks in the capital carried out in the run-up to parliamentary elections last month.
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"They don't care about our children," he said, lashing out at "those murderers who live in the DRC (and) in South Africa" -- a reference to exiled Hutu extremists linked to the 1994 genocide as well as other opponents.
The M23 rebel group was founded by former Tutsi rebels who were incorporated into the Congolese army under a 2009 peace deal but who turned their guns on their former comrades in 2012.
Kagame repeated denials of covert support for the M23, and described the sanctions as an "insult".
"I don't understand why Rwanda is treated... With such injustice," he said. "Rwanda is going to be judged and held accountable for the mistakes made by others.