Libya announced on 8 December that it was stepping down as the one-year rotating president of the AMU in protest at what it said was other member states breaching the organisation's rules, including accepting to take part in military exercises with Israel and Nato.
But foreign ministers of Algeria, Morocco, Tunisia and Mauritania pleaded with Libyan leader Muammar al-Qadhafi at a weekend meeting in Tripoli.
"In response to the desire of his brothers, leaders of the union member states, the leader (al-Qadhafi) agreed to continue his presidency of the union until the summit convenes, which date will be fixed as soon as possible," a joint foreign ministers' statement published by Jana said.
The AMU presidency is supposed to rotate on a yearly basis but Algeria held it from 1994 until 2003 because of disagreement between members.
The AMU was set up to create a free trade zone to mirror the European Union and promote greater social and political integration. An Algiers summit in December 2003 was cancelled at the last minute when three of the five heads of state declined to attend.
Since its creation in 1989 with much ado, the union has held only one summit in 1994. Regional disputes have held the organisation back, in particular that between Algeria and
Morocco over the disputed territory of Western Sahara. Earlier this year Mauritania accused Libya of backing attempts to overthrow its president.