Drafted by France, the resolution tasks UN Secretary- General Ban Ki-moon with drawing up within 15 days a list of options for the proposed police force, in consultation with the Burundian government and the African Union.
The council is under pressure to take action in Burundi where the descent into violence has raised fears of mass atrocities, similar to those that convulsed neighboring Rwanda in 1994.
"We need the United Nations to be more present on the ground," French Ambassador Francois Delattre told the council.
The vote capped days of tough negotiations between France and the United States over the wording of the resolution, the second measure adopted by the council over the Burundi crisis.
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The resolution provides for the "deployment of a United Nations police contribution to increase the United Nations capacity to monitor the security situation, promote the respect of human rights and advance rule of law" in Burundi.
Burundi has been in turmoil since President Pierre Nkurunziza announced plans last April to run for a third term, which he went on to win.