Ten Council members voted in favor of the resolution Thursday with no votes against it. Five members -- Brazil, China, Germany, India, and Russia -- abstained.
The resolution authorizes U.N. members to take "all necessary measures" to protect civilians, including a ban on all flights over Libya.
The resolution expresses grave concern at the deteriorating situation in Libya, where rebels have been trying to topple long-time leader Moammar Gadhafi with deadly results. It also calls for an immediate cease-fire and a total end to all violence against civilians.
Mr. Gadhafi has warned the rebels in Benghazi to surrender or face an imminent attack. He said his forces will show no mercy and search every home for those he calls traitors.
French Prime Minister Francois Fillon says his government supports military action against Libya as quickly as possible. France, Britain, and Lebanon were the three sponsors of Thursday's resolution.
Libyan state television warned that any military action against the country will expose all Mediterranean air and maritime traffic to "danger."
Libyan rebels say they shot down two government warplanes that tried to bomb Benghazi Thursday. Pro-Gadhafi forces launched airstrikes on nearby Ajdabiya and surrounded rebels holding out in the town, located south of Benghazi.