The resolution was passed on Friday by 15-0 votes after Russia – its initiator - softened the original text considerably in the face of objections from Algeria and Pakistan.
The original Russian draft recommended a UN blacklist of individuals, groups and entities involved in terrorism, who would be subject to an asset freeze, an arms embargo and expedited extradition.
Currently such penalties apply only to al-Qaida and the Taliban.
The final text creates a working group to consider such measures, but does not mention the blacklist.
The resolution calls on states to "deny safe haven and bring to justice" any person who supports or participates in the "financing, planning, preparation or commission of terrorist acts".
Russia proposed the resolution
after the Beslan school siege
The anti-terror proposals were first announced by Russian Foreign Minister Sergei Lavrov in a speech to the UN General Assembly last month in the wake of a spate of attacks by Chechen separatists, including the bombing of two airliners and the deadly Beslan school siege.
The measure also attempts to define terrorism or "criminal acts", something that has eluded the UN General Assembly for years in trying to draft an omnibus treaty on the subject.
Algeria and Pakistan, the two Islamic nations on the Security Council, opposed any wording that would exclude "legitimate resistance", one of the main obstacles the General Assembly faced in previous years.
"While we all agree that acts against civilians are terrorist acts, there is no similar consensus on what are the rights of people struggling against foreign occupation," said Pakistan's UN ambassador, Munir Akram.
Lavrov argued that targeting only al-Qaida and the Taliban in Security Council resolutions showed a double standard.
"Those who slaughtered children in Beslan and hijacked airplanes to attack America are creatures of the same breed," he said.