(CNN) -- Yemen's President Ali Abdullah Saleh will not seek re-election once his current term ends in 2013, he said Wednesday, after more than three decades in office.

He won't install his son to replace him, he said. He also has asked his political opponents "to re-engage in dialogue in hopes of reaching a sustainable and reconcilable political agreement," the Yemeni government said.

Saleh made the announcement as unprecedented protests sweep across North Africa and the Middle East. The demonstrations have forced Tunisia's president from office, and they prompted Egyptian President Hosni Mubarak to say Tuesday he would not run for re-election this year.

King Abdullah of Jordan, meanwhile, has sacked his government and appointed a new prime minister in the face of protests there.

In Yemen, Saleh had called an emergency parliamentary meeting ahead of a "day of rage" protests scheduled for Thursday.

The protests -- which have also caught on to various extents in Algeria and Sudan -- have proved to be "a real watershed event for the Arab world," said Blake Hounshell, managing editor of Foreign Policy magazine. "It's really unprecedented."

Saleh has been in office for 32 years and was last re-elected in 2006.

High-ranking officials around him have started obtaining ordinary passports for themselves and their families -- in addition to the official diplomatic ones they already carry -- as the unrest spreads, Arab diplomatic sources in the capital of Sanaa told CNN.

"There is a lot of trepidation here and no one wants to be in the situation that Ben Ali found himself in after he was forced flee," one source said, declining to be named because of the sensitivity of the situation.

The Tunisian government recently canceled the official passports of deposed leader Zine El Abedine Ben Ali and his family.

In recent weeks, thousands of people have taken to the streets in Yemen demanding the kind of change that forced Ben Ali from office last month.

Some of the protesters have called for Saleh to step down as president.

Earlier this year, Yemen's parliament began debating proposed amendments to the country's constitution. The measures, which would cancel presidential term limits, have sparked concerns among the opposition that Saleh might try to appoint himself president for life.

On Wednesday, Saleh said he has requested his party to freeze debate on the proposed amendments until a consensus is reached.

The opposition coalition, Joint Meeting Parties (JMP), said the president's speech was not enough and called on its followers to continue with Thursday's planned march, said Hakim Almasmari, editor in chief of the Yemen Post.

A day earlier, the president also ordered the release of journalist Abdul Elah Haidar Shaye who was sentenced to five years in jail last month after he was convicted of collaborating with al Qaeda in Yemen, according to the country's official news agency, SABA.

CNN's Nima Elbagir contributed to this report.