The United Nations has set up a board of inquiry to investigate the deaths in March of two UN experts and mass graves.
In a unanimous statement, the council also told the Kinshasa government and the opposition to step up efforts to implement a New Year's Eve agreement aimed at paving the way to elections.
Council members "stressed the need for a swift and full investigation into the killing" of the two UN experts and "underlined the need for full cooperation from the government of the DRC," the statement drafted by France said.
The United Nations has set up a board of inquiry to investigate the deaths in March of Michael Sharp, an American, and Zaida Catalan, a dual Swedish-Chilean national.
They were members of a UN panel of experts seeking to investigate reports of more than 40 mass graves found in the central Kasai region when they were abducted and shot dead. One of the victims was also beheaded.
The council said it would "closely monitor" investigations by the government, working with the UN mission in the DR Congo and the African Union on rights abuses in Kasai.
Kasai has seen a major spike in violence since September that has killed at least 400 in an uprising that erupted when government forces killed Kamwina Nsapu, a tribal chief and militia leader, who had rebelled against President Joseph Kabila.
The UN has accused the Nsapu rebels of using child soldiers and committing several atrocities, while also denouncing the disproportionate use of force by the military.
The council called for the political agreement to be quickly implemented "in order to organize peaceful, credible, inclusive and timely elections, no later than December 2017, leading to a peaceful transfer of power" in the vast resource-rich African country.
After months of violence, the influential Catholic Church brokered a deal to pave the way for elections, but the agreement has since been bogged down in disputes.
Elections would bring an end to the rule of President Joseph Kabila, in power since 2001.