Yemen's governing party has again failed to agree on a candidate for presidential elections in September.
Pro-government papers are urging President Saleh to stay on
General People's Congress members want incumbent Ali Abdullah Saleh to stand again, but he has repeatedly said he will not seek another term in office.
The official Yemen News Agency said a second day of talks had failed to persuade him to change his mind.
President Saleh has led the country since the unification of North and South Yemen in 1990.
Before that, he was president of North Yemen for 12 years, giving him nearly three decades of uninterrupted power.
"I am neither ill nor incapable of shouldering the responsibility," Mr Saleh said in a speech on Wednesday.
"But I... achieved Yemen's reunification, the settlement of borders, and the introduction of comprehensive development.
"Now I want to preserve this achievement when I hand over power peacefully to the Yemeni people."
The official news agency said the talks would now continue indefinitely until agreement was reached.