The U.S.-allied Ali Abdullah Saleh, who has been in power for nearly 32 years, spoke to lawmakers in both houses of the assembly on the eve of mass rallies that the opposition has called for Thursday in all Yemeni provinces.
"I won't seek to extend my presidency for another term or have my son inherit it," Saleh told the parliament.
Saleh has earlier tried to defuse simmering tensions in Yemen by raising salaries for the army and by denying opponents' claims he plans to install his son as his successor.
Complete Coverage: Anger in the Arab World
But that hasn't stopped critics of his rule from taking to the streets of the capital, Sanaa. In January, tens of thousands gathered in days of demonstrations, boldly calling for Saleh to step down a red line that few dissenters had previously dared to cross here.
Saleh's current term in office expires in 2013 but proposed amendments to the constitution could let him remain in power for two additional terms of ten years.
The repercussions of Tunisia's government collapsing and Egypt's mass protests calling for the ouster of President Hosni Mubarak were being felt around the Mideast, as other authoritarian governments fearing popular discontent pre-emptively tried to burnish their democratic image.
Jordan's Tuesday in the face of smaller street protests, named an ex-prime minister to form a new Cabinet and ordered him to launch political reforms. The Palestinian Cabinet in the West Bank said it would hold long-promised municipal elections "as soon as possible."
Following the start of the regional unrest, Saleh ordered income taxes slashed in half and instructed his government to control prices. He deployed anti-riot police and soldiers to several key areas in Sanaa and its surroundings to prevent riots.
But the street protests, led by opposition members and youth activists, continued, adding to the threats to Yemen's stability.
In the parliament Wednesday, Saleh called upon the opposition to meet for a dialogue on political reforms and their demands.
Opposition spokesman Mohammed al-Sabri rejected the call for dialogue and expressed doubts about Saleh's pledge not to seek re-election. Al-Sabri said Saleh made a similar promise in 2006, but then failed to fulfill it, ran again and was re-elected.
"The calls for dialogue are not serious and are merely meant to be tranquilizers," al-Sabri told The Associated Press. He added that the opposition parties would meet later Wednesday to prepare an official response to Saleh's announcement.
Yemen is the Arab world's most impoverished nation and has become a haven for al Qaeda militants. Saleh's government is riddled with corruption, has little control outside the capital, and its main source of income oil could run dry in a decade.
Nearly half of Yemen's population lives below the poverty line of $2 a day and doesn't have access to proper sanitation. Less than a tenth of the roads are paved. Tens of thousands have been displaced from their homes by conflict, flooding the cities. The country is enduring a rebellion in the north and a secessionist movement in the south.
Saleh's ruling National Congress Party has 240 seats in the 301-member parliament. The opposition is a broad specter of mainly leftist and Islamic parties the most prominent being the Socialists, who governed south Yemen before the north and the south merged in 1990, and the influential fundamentalist Islamic Islah Party. U.S. considers one of Islah's leaders, Sheik Abdul-Majid al-Zindani, an al Qaeda-linked terrorist.
As in Egypt, where Mubarak's son Gamal was believed to be preparing to succeed his father, Saleh's son Ahmed an army brigadier and head of the presidential guard and special forces was also believed to be groomed for succession.
Yemen has been the site of numerous anti-U.S. attacks dating back to the 2000 bombing of the USS Cole in Aden harbor, which killed 17 American sailors. Radical cleric Anwar al-Awlaki, thought to be hiding in Yemen, is suspected of having inspired some of those attacks, including the deadly 2009 shooting rampage at Fort Hood, Texas.
Al Qaeda in the Arabian Peninsula was also thought to be behind the attempted bombing of an American airliner landing in Detroit on Christmas Day 2009.