Thousands of people have attended the launch of a new Nigerian opposition party in the capital, Abuja.
Mr Obasanjo's second term in office ends next year
The Advanced Congress of Democrats has attracted critics of plans to change the constitution to let President Olusegun Obasanjo seek a third term.
ACD supporters wore T-shirts bearing slogans such as "No third term" and chanted "Democracy forever".
Correspondents say Vice-President Atiku Abubakar, who opposes the third term, is believed to back the new party.
The ACD launch was broadcast live on state television, in what correspondents say is unusual coverage for an opposition party.
Earlier this week, a group of ruling party officials in Mr Abubakar's home state of Adamawa said they had suspended the vice-president because he was sponsoring the ACD.
But his spokesman said the suspension was "ridiculous".
Lagos State governor Bola Tinubu was at the ACD launch and said his Alliance for Democracy was considering a merger with the new party to create a strong opposition grouping.
Vice-President Atiku Abubakar has helped Obasanjo win two elections
"We should not change our constitution to suit the desire of a single leader who has trampled on democracy and the rule of law," he told Reuters news agency.
"African leaders must know when to leave power. We cannot follow Zimbabwe."
Mr Obasanjo has not publicly said whether he wants to remain in office but both he and the vice-president are believed to want to contest elections due next year.
Mr Obasanjo and Mr Abubakar have been president and vice-president since the end of military rule in 1999.
Correspondents say that if the opposition to Mr Obasanjo can unite, it could provide a serious challenge to his People's Democratic Party in elections due next year.
The AD draws much of its support from the south-west, while Mr Abubakar is popular in the mainly Muslim north.
The National Assembly is due to consider more than 100 proposed constitutional amendments, including whether to extend the limit on a president's term in office from two to three terms.
Opponents of the constitutional change argue that the presidency needs to rotate among people from different regions and ethnic groups.
Mr Obasanjo is a Christian from the south-west while Mr Abubakar is a northern Muslim.