The UNSC meeting also focussed on the 15th report of the Secretary-General on the threat posed by ISIL (Da'esh) to international peace and security and the range of United Nations efforts in support of member states in countering the threat.
The council's appeal came in a presidential statement at the end of a day-long discussion on crimes against women.
Sri Lanka on Friday announced withdrawal of its nominee Jayantha Dhanapala from the race for the post of next United Nations Secretary-General following his consistent bad performance in the last three straw polls.
Burns denied that he was against Tharoor as UNSG.
South Korean Foreign Minister Ban Ki-moon is set to be formally appointed the eighth UN secretary general at the world body's General Assembly meeting on Friday
India on Thursday urged United Nations Secretary General Ban Ki-Moon to ask member nations not to cut down financial and technical aid for public health initiatives across the globe.
India will convey its views on major regional and global issues apart from strongly pitching for an expansion of the Security Council with its inclusion as a permanent member during the four-day visit of United Nations Secretary General Ban Ki-moon, who arrived in New Delhi on Thursday.
Annan was the first black African to take up the role of the world's top diplomat
United Nations General Assembly on Friday appointed Antonio Guterres as the UN Secretary General for a second term beginning January 1, 2022, days after the powerful Security Council unanimously recommended his name to the 193-member body for re-election.
The race for the UN secretary-general for 2022-2027 is already over and another term for Antonio Guterres is a foregone conclusion, observes Ambassador T P Sreenivasan.
The 15-member Council held a formal vote here to elect Guterres, the former UN High Commissioner for refugees had emerged as the "clear favourite" to succeed Ban Ki-moon, 72, as the 9th Secretary General.
The report covers 20 countries, including war-torn Syria, Afghanistan, and Yemen and also the situation in India, the Philippines and Nigeria.