Saleh has ruled Yemen since unification in 1990 after 12 years as president of North Yemen. His declaration came during a speech to mark the 27th anniversary of his rise to power.
"I will not contest the elections," he told a group of politicians, diplomats and journalists, referring to the polls due for September 2006.
"I hope that all political parties - including the opposition and the [governing] General People's Congress - find young leaders to compete in the elections because we have to train ourselves in the practice of peaceful succession."
Some political analysts took Saleh at his word, saying Yemenis should be prepared for a new president next year.
Other analysts, however, said Saleh was probably pandering to calls for reform by the United States which has pressed Arab allies, including Egypt's President Hosni Mubarak, to allow more political freedom.
"I hope that all political parties find young leaders to compete in the elections because we have to train ourselves in the practice of peaceful succession"
Ali Abdullah Saleh,
Since the 11 September 2001 attacks on the US, Yemen has cooperated closely with the US on the "war on terror".
Yemen is the ancestral home of al-Qaida leader Osama bin Laden.
Saleh's current seven-year presidential term ends next year. The constitution allows him to take office - if he wins - for one more term.
Saleh won Yemen's first direct presidential election in 1999 with an overwhelming majority. His party still holds most of the seats in parliament, which must first approve candidates before they can run in the election.