The Assembly of States Parties is presided over by its Bureau and President, elected for three year terms. It possesses a representative character, accounting for geographical distribution and representation of various legal systems. The Bureau meets regularly throughout the year in both New York and The Hague to assist the ASP in the discharge of its responsibilities and reports to the ASP on its activities at each session. The President calls for and leads the meetings of the Bureau, and chairs the ASP sessions.

The President of the ASP is currently Ms. Tiina Intelmann of Estonia. She has been elected as President for a three-year term beginning November 2011. The two current vice-presidents are Mr. Marcus Börlin of Switzerland and Mr. Ken Kanda of Ghana.

The Bureau of the ASP is currently composed of the following other members: Belgium Canada, Finland, Portugal, Republic of Korea, Japan, Samoa, Argentina, Brazil, Chile, Gabon, Nigeria, South Africa, Trinidad and Tobago, Uganda, Czech Republic, Poland and Slovakia.

The first President of the ASP was Ambassador Prince Zeid Ra'ad Zeid Al Hussein of Jordan, the second was Mr. Bruno Stagno Ugarte of Costa Rica and the third was Mr. Christian Wenaweser of Liechtenstein.