He had been expected to add his signature on Saturday after his officials said the deal, brokered by Gulf Arab states, had been accepted.
Mr Saleh reportedly said he would only sign the agreement in his capacity as head of the ruling party, but opposition spokesmen insist he must sign as president, the BBC says.
The Gulf states' mediator is now believed to have left the capital, Sanaa.
New clashes in the Yemeni port of Aden have left three people dead.
Officials say two of the dead were members of the security forces, shot while trying to dismantle road-blocks set up by protesters in the al-Mansoura district.
