"It is unacceptable and illogical to override the constitutional legality or for the minority to impose its will on the majority of the people," Saleh's General People's Congress said in a meeting.
The GPC accused the opposition of having "closed the door to dialogue and sought isolation," and said the crowds who took part in a rally of solidarity with Saleh on Friday numbered as many as three million.
"Power will only be handed over to someone chosen by the people through elections, the only way for a peaceful transition of power," party spokesman Tareq al-Shami told AFP on the morning after the meeting.
"The people have had their say," Shami said. "In the absence of a national agreement, we are committed to the constitutional process, which provides for presidential elections in 2013."
Saleh himself said he would hand over power but only to "safe hands," in a defiant speech to his massed supporters, a day after talks with a top defector apparently failed to defuse the crisis.
"You are the ones who will be handed power," the Yemeni strongman told his supporters.
In the south of the country, a security source said army soldiers killed six suspected Al-Qaeda members who attacked a post at a power plant in Loder, a town in restive Abyan province, a stronghold of the Islamist militants.
Government forces and Al-Qaeda militants fought a pitched battle in the town of Loder in August 2010, when at least 33 people were killed, including 19 militants.
Analysts have said Saleh's role as a key US anti-Qaeda ally has likely contributed to Washington's relatively muted response to deadly crackdowns on pro-democracy protests in Yemen.
The president, whose concessions and offers to stand down by the end of 2011 have been snubbed by the opposition, renewed his invitation for youths at the forefront of the protests to join a dialogue.
"I am ready to talk to you and to form a political party for the youths," said Saleh, 69, who has ruled Yemen since 1978.
In behind-the-scenes talks aimed at averting more bloodshed, Saleh and top dissident General Ali Mohsen al-Ahmar, considered the second strongest man in Yemen, failed to strike a deal on Thursday night, the two sides said.
Defections to the opposition accelerated after Saleh regime loyalists opened fire during a protest in Sanaa on March 18, killing 52 people and sparking worldwide condemnation.
Ahmar, a regional army commander who has vowed to defend the protesters, is leading efforts to form a transitional council grouping all sides, according to sources close to the secret negotiations.
With hundreds of thousands of rival demonstrators on Sanaa's streets on Friday, soldiers fired warning shots to prevent loyalists from attacking anti-regime protesters. There were no reports of casualties.
Many in the anti-regime camp brandished football referee-style red cards signaling it was time for Saleh to go.
---------------------------------------------------------------------------------------