The council members welcomed the signing of the Peace and National Partnership Agreement in Yemen, describing it as the best means to stabilise the situation and prevent further violence, Xinhua reported citing the statement.
The Yemeni government and Houthi rebels agreed Sunday night to a ceasefire.
The peace agreement put an end to deadly clashes between the rebels and the army which broke out on Sep 16 in north-western Sanaa and left more than 200 people killed, including about 50 civilians.
In Tuesday's statement, the 15-nation council underlined that President Abd-Rabbu Mansour Hadi is the legitimate authority based on election results.
"All parties and political actors in Yemen must unite behind President Hadi to keep the country on track towards stability and security," said the statement.