The 15-member council backed plans by Secretary-General Ban Ki-moon to send a high-level UN official on an urgent mission to ease the Burundi crisis.
The council issued an appeal for dialogue after senior UN officials warned during a closed-door emergency meeting called by France that the violence was worsening in the central African country, AFP reported.
"Council members expressed deep concern on the political and security situation in Burundi and called for the immediate resumption of inclusive dialogue in order to achieve a lasting peace," Nigerian Ambassador Joy Ogwu told reporters following the meeting.
The ambassador, whose country holds the council presidency, said Ban would be sending an envoy soon.
The recent killing of a top general and the attempted murder of a leading human rights activist are seen as a dangerous escalation in the conflict sparked by President Pierre Nkurunziza's bid to win a third term in office.
Nkurunziza, in power since 2005, was declared the outright winner of elections last month that were boycotted by the opposition and condemned internationally as deeply flawed.
UN rights official Ivan Simonovic told the council that at least 94 people have been killed since the crisis began in April with Nkurunziza's decision to seek a third term, according to diplomats at the meeting.
About 600 people have been arrested or detained and some 40 cases of torture during police custody have been reported, he said.
Simonovic said there was a "new worrying trend of killing of ruling party members" targeted for reprisals and score-settling following the election, a diplomat said.
The United States last week threatened to impose sanctions such as travel bans on those deemed responsible for the violence in Burundi.
Talks between the government and the opposition broke down on July 19.