Ban, who has been leading in the race to succeed current Secretary-General Kofi Annan, led Thursday with 13 votes in his favor, one against him and one undecided.
The council will take another, more informative, informal vote on Monday, when the preferences of the five permanent members, Britain, China, France, Russia and the United States, will be revealed.
The selected nominee will need at least nine positive votes, and no dissent from the permanent five, to be recommended to the U.N. General Assembly, whose members then cast their ballots.
The date for the official vote has not been set, but U.S. Ambassador John Bolton has been pushing for an early October election.
Indian Shashi Tharoor trailed Ban with eight positive votes.
With seven votes in her favor, Latvian President Vaira Vike-Freiberga came in third, with Sri Lankan Jayantha Dhanapala, Jordan's Prince Zeid Ra'ad Zeid Al-Hussein and Afghanistan's Ashraf Ghani all garnering three positive votes.