A top military official who defected to the opposition this week met privately with President Ali Abdullah Saleh Thursday to suggest ways he could leave power, an aide who attended the meeting said.
Saleh rejected the offer, lashing out instead out at the protesters threatening his 32-year rule.
"Even if we entered with them now into an understanding, the situation will be worse than it is now," Saleh said of the opposition. "We will cling to constitutional legitimacy and we will preserve the security, independence and safety of the Yemeni republic with all means possible."
The opposition's widening demands reflect the perception that Saleh's regime has been badly weakened by weeks of unrelenting protests and the defection to the opposition of a number of powerful officials, including members of the president's inner circle.
The organizers say they hope several million people will turn out for Friday prayers in public squares and follow them with demonstrators against Saleh.
On Thursday night, security forces deployed heavily throughout the capital, raising the specter of confrontations.
The leaders of the "Civil Coalition for Peaceful Revolution" - an umbrella group for several pro-reform organizations - told a news conference they also wanted to limit future presidents to two four-year terms in office, and to create an interim presidential council of nine civilians to run the country until legislative and presidential elections are held.
The leader of Yemen's largest tribe sided with Saleh's opponents, calling on him to step down immediately and refrain from further violence against protesters.
The decision by the widely respected Sheik Sinan Abu Lohoum, 80, was announced in a statement issued from the United States, where he is receiving medical treatment. It was read to protesters gathered at a central Sanaa square that has become the epicenter of the protests.
Members of Abu Lohoum's immediate family confirmed the statement's authenticity.
Abu Lohoum's Baqeel tribe is the larger of two that follow the Zaidi offshoot of Shiite Islam. The other - Saleh's own Hashid tribe - has already backed the opposition.
Several senior military commanders, lawmakers, Cabinet ministers, diplomats and provincial governors have also defected to the opposition over the last week.
"Those from the security and military institutions who have joined the youth revolution are most welcome," said one of the youth leaders, Nizar al-Jeneid. "We call on others to follow their example," he added before he warned that anyone among them found to have been corrupt should be held accountable.
Thursday afternoon, the most powerful man to emerge as a likely successor met with Saleh to suggest ways for him to leave power, an aid to Maj. Gen. Ali Mohsen al-Ahmar told The Associated Press.
Al-Ahmar defected to the opposition this week and deployed his troops at the Sanaa square where protesters have camped out for weeks.
In the Thursday meeting at the vice president's residence, Al-Ahmar suggested that Saleh transfer power to his vice president, Abd Rabou Mansour, or to a transitional council that would run the country until new parliamentary elections, said the aide, who attended the meeting. An official in the vice president's office also confirmed the contents of the meeting. Both spoke on condition of anonymity because the talks were private.
Saleh rejected the offer, later appearing on state TV lashing out at protesters in a meeting with military and government officials.
He denied the protesters were peaceful, saying they had surrounded banks and sought to attack military bases.
"Is this the shared language that peacefully strives for change?" he asked. "They won't be with the peaceful transition of power or with elections."
Saleh has repeatedly sought to appease the protesters, but to no avail.
Over the past month, he has offered not to run again when his current term ends in 2013, then offered this week to step down by the end of the year and open a dialogue with the leaders of the demonstrators.
At the same time, Saleh has stepped up his violent crackdown. His security forces shot dead more than 40 demonstrators in Sanaa last Friday, but the bloodshed only escalated the defections and hardened the protesters' rejection of anything but his immediate departure.
Yemen's legislature granted Saleh's request for a 30-day state of emergency on Wednesday in a vote the opposition called illegal.
The decree allows media censorship, gives wide powers to censor mail, tap phone lines, search homes and arrest and detain suspects without judicial process. The state of emergency declaration appeared to signal that Saleh intends to dig in and try to crush his opponents.