U.N. Secretary General Ban Ki-moon told African leaders on Saturday they should not use legal loopholes or undemocratic constitutional changes to "cling to power", and that they should respect term limits.
Ban was addressing a two-day summit the African Union, a group of 54 states where several leaders have been in power for decades, some have changed constitutions so they can stay on and others are accused of seeking to remove limits.
The debate about term limits has gained momentum after triggering unrest in places such as Burundi and Congo Republic.
"Leaders should never use undemocratic constitutional changes and legal loopholes to cling to power. We have all seen the tragic consequences when they do," Ban told the gathered presidents, including Zimbabwe's veteran leader Robert Mugabe.
It echoed remarks made by U.S. President Barack Obama in the same AU hall on a trip to Ethiopia in July.
Mugabe, who turns 91 in February and the only leader Zimbabweans have known since 1980, made one of his regular swipes at Western powers who he accuses of still harbouring colonial ambitions and of monopolising power at the United Nations.
One of the top items on this summit's agenda is the crisis in Burundi, where violence erupted after President Pierre Nkurunziza announced his bid for a third term that opponents said was illegal. He won a disputed election in July.
Supporters cite a court ruling that said he could run.
In neighbouring Rwanda, a constitutional change approved in a referendum means President Paul Kagame, who has been in office since 2000 and effectively in power far longer, can now run again in 2017 and could stay on until 2034 if he wishes.
Western powers criticised Kagame for not stepping aside, saying he should set an example.
Uganda's Western allies have said President Yoweri Museveni, bidding for another term in a February vote after three decades in office, should consider quitting although the Ugandan constitution does not set any term limits.
"Leaders must protect their people, not themselves," Ban said. "I commend those leaders who committed to stepping aside and respect constitutional term limits."
Tanzania's Jakaya Kikwete left office after a maximum two terms last year. However, the candidate of Kikwete's CCM party that been in power for more than half a century won the vote.