Yemen's longtime president, Ali Abdullah Saleh, offered Tuesday to step down after parliamentary elections in January as more officials and military units abandoned him to support anti-government protesters.

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TUNIS, Tunisia — In a last-ditch gambit to stay in power, Yemen’s longtime president, Ali Abdullah Saleh, offered Tuesday to step down after parliamentary elections in January as more officials and military units abandoned him to support anti-government protesters.

The protesters have demanded that Saleh resign immediately, but he said that doing so would incite “civil war” in his impoverished and deeply tribal Arabian Peninsula nation.

But Mohammed al Sabry, a spokesman for Yemen’s main opposition coalition, said it “rejects the offer” of Saleh’s future departure, news agencies said.

In a potentially explosive split, rival factions of the military have deployed tanks in the capital Sanaa — with units commanded by Saleh’s son protecting the president’s palace, and units loyal to a top dissident commander protecting the protesters.

The defection on Monday of that commander, Maj. Gen. Ali Mohsen al-Ahmar, a powerful regime insider who commands the army’s 1st Armored Division, has been seen by many as a major turning point toward a potentially rapid end for Saleh’s nearly 32-year rule.

Saleh, a U.S. ally in the fight against terrorism and recipient of some $300 million a year in military support, now seems to be the likeliest domino to fall next in the historic tide of uprisings.

The question is whether the Yemeni chapter of the uprisings will read more like Egypt — where the resignation of President Hosni Mubarak set the country on a relatively stable, if still uncertain, move toward democracy — or like Libya, which has seen brutal fighting between armed camps.

Already, clashes broke out late Monday between Saleh’s Republican Guard and dissident army units in the far eastern corner of the country. On Tuesday, Republican Guard tanks surrounded a key air base in the western Red Sea coastal city of Hodeida after its commander — Col. Ahmed al-Sanhani, a member of Saleh’s own clan — announced he was joining the opposition.

Weeks ago, Saleh tried to stave off unrest by promising not to run for re-election when his term expires in 2013 — he made the same promise in 2005 — but support from within his government has rapidly eroded since a shocking burst of violence Friday, when his armed forces and snipers opened fire on protesters and killed 52 people.

A European diplomat, who requested anonymity to speak more frankly, said it is “probably just a matter of time now” before Saleh leaves office. Mohsen’s defection “is fundamentally the beginning of the end game,” he said.

The United States again expressed concern Tuesday that a power vacuum in Yemen could provide an opening for terrorist groups, including al-Qaida’s local affiliate, called al-Qaida in the Arabian Peninsula, which since 2009 has mounted multiple terrorist plots against the United States.

Neighboring Saudi Arabia, which has backed Saleh against his internal opponents, also is nervous.

“We are obviously concerned about the instability in Yemen,” Defense Secretary Robert Gates, traveling in Russia, said Tuesday. “We consider al-Qaida in the Arabian Peninsula, which is largely located in Yemen, to perhaps be the most dangerous of all of the franchises of al-Qaida right now.”

Information from The New York Times and The Associated Press

is included in this report.