Yemen's opposition, meanwhile, called for mass protests following another round of deadly clashes with police, as talks appeared to have stalled between Gulf mediators and Saleh's envoys.
"We will continue to resist (...) undaunted and committed to constitutional legitimacy, while rejecting the plots and coups," Saba quoted the embattled president as saying.
Addressing a women's group in Sanaa, Saleh reiterated he would relinquish power only through elections.
"Let those who want to attain power rely on the ballot box. Change can only come about through elections and within the framework of constitutional legitimacy," said Saleh, whose term runs until 2013.
Saleh's statement comes after members of the UN Security Council failed to come up with a joint statement on Yemen after adding the country's crisis to their agenda for the first time.
Youth groups called for nationwide marches by millions of people in protest at the killing of protesters on Tuesday, stressing their rejection of any deal that excludes Saleh's immediate departure.
Confrontations raged on between security forces and anti-Saleh protesters, with medics and witnesses reporting that eight people were shot dead since yesterday, including a passer-by and a policeman.
One protester was killed when a gunman on a motorbike opened fire early today at demonstrators staging a sit-in at Al-Nasr Square in the western Red Sea city of Hudaydah.
The assailant managed to escape after also wounding about eight other protesters, most of whom had been asleep.
Also on Wednesday, a policeman was shot dead during clashes between police and protesters in the main southern port city of Aden, while five demonstrators were shot dead in the capital Sanaa yesterday.
Foreign ministers of the Gulf Cooperation Council (GCC) held talks yesterday with representatives of Saleh's regime as part of efforts to hammer out a deal under which the veteran president would step down.
But the meeting in Abu Dhabi appeared to have made no significant progress.
A brief, vague statement issued afterwards referred to the talks as "constructive," vowing to "exert more effort to preserve security, stability and the unity of the Yemeni state."