Under the agreement reached on New Year's Eve, elections are to be held this year in the large mineral-rich African country that would be the DR Congo's first democratic transition.
Concerns are growing however that the deal is unraveling after the head of the electoral commission said this month that the vote will likely not be held this year.
In a unanimous statement drafted by France, the council warned that "unless political actors demonstrate renewed good faith and political will to deliver on the promises they made to their people on New Year's Eve 2016, the DRC and the wider region are set to face an increased risk of insecurity and instability."
Opposition leaders said at the weekend that Kabila must agree by the end of September to an election date or else they will no longer recognize him as president as of October 1.
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In the statement, the council stressed the "urgency of swift implementation" in order to organize "peaceful, credible inclusive and timely elections, no later than December 2017" and achieve a peaceful transfer of power.
At a council meeting earlier this month, the United States demanded that the electoral commission immediately publish an electoral calendar and specifically a date for the presidential vote.
Washington threatened unilateral sanctions and said the Security Council should consider imposing measures to pile pressure on all sides over the elections delay.
The council also condemned violence in the Kasai region, where UN officials say they have uncovered dozens of mass graves and two UN experts were killed while investigating the killings.