The resolution, which comes a day after Libyan strongman Muammar Gaddafi was killed, stresses that Gulf Cooperation Council's initiative should be implemented that calls for the president to transfer power to his vice-president followed by the formation of an interim government, a new constitution and elections.
This is "essential for an inclusive, orderly and Yemeni-led process of political transition."
Condemning human rights violations and the excessive use of force by the Yemeni authorities against peaceful protesters in the country's eight-month uprising, the Security Council said all sides should quickly implement a regional plan for an orderly transition of power.
"Now is the time for government and opposition leaders to live up to their responsibilities and reach an agreement. The resolution is clear in this regard. It calls for action without further delay."
The Council urged all opposition groups to "commit to playing a full and constructive part in the agreement and implementation" of the initiative and refrain from violence and the use of force to achieve political aims.
It called for all those responsible for violence and human rights abuses to be held accountable.
"The Yemeni sides have debated the key elements for a transition settlement for quite some time," Under Secretary-General for Political Affairs Lynn Pascoe told reporters here after adoption of the resolution.
In the resolution, the 15-member body noted that hundreds of people – mainly civilians, including women and children – had died in months of violence between supporters and opponents of Saleh, and demanded that the authorities immediately end attacks by security forces against civilians.
The resolution also voiced concern over presence in the country of the terrorist group al-Qaida in the Arabian Peninsula, and the risk of new terrorist attacks in parts of Yemen. The Council also called on the international community to provide humanitarian aid to the country.
Last week, Secretary-General Ban Ki-moon's Special Adviser on Yemen Jamal Benomar warned the Council that security had deteriorated "very dramatically", with five or six provinces out of government control, al-Qaida militants holding three cities and an important geographic area in the south, and Sana'a, the capital, split between rival forces.
Pascoe said the Secretary-General welcomes the adoption of the Security Council resolution on Yemen.
"This is a clear sign of deepening international concern about the absence of a political settlement in Yemen, and how this is contributing to a rapid deterioration in the situation in the country."