The council met Monday but did not reach a decision about the force's mandate, which is due to expire February 15.
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Former U.N. Secretary General Kofi Annan had called for a 12-month extension before leaving his post last year.
After Monday's meeting, Russia's U.N. ambassador Vitaly Churkin said that some of the council's 15 members continue to oppose extending the force.
There are almost 8,000 U.N. peacekeepers in Haiti currently working to root out violent gangs.
The peacekeepers were deployed in 2004 after former President Jean-Bertrand Aristide was ousted in an uprising.
Some information for this report was provided by AFP, AP and Reuters.