Faced with mass protests since January, Saleh, who had said he would stay in office until his term runs out in September 2013 but not run again, has offered to quit by January after a parliamentary poll, according to a senior official.
The official, speaking on condition of anonymity, told AFP it was part of an initiative by Saleh, who turned 69 on Monday and has been in power since 1978, "to switch to a parliamentary system."
A popular campaign to depose Saleh kicked off two months ago amid the mass protests in Egypt that led to the ouster of president Hosni Mubarak.
A potential turning point came on Friday, with the slaughter of 52 people gunned down by regime loyalists in Sanaa during an anti-regime demonstration that has accelerated defections from Saleh's camp.
Joining widespread international condemnation of the mass killing of civilians, the Arab League urged Sanaa on Tuesday to make "concerted efforts to safeguard national unity and the right to free expression."
With tanks deployed outside key installations in Sanaa, Saleh warned that a coup attempt in Yemen could spark civil war, a day after two soldiers were reported killed in a clash between rival units of the Yemeni military.
US Defence Secretary William Gates, meanwhile, said in Moscow that Yemen's "instability and diversion of attention from dealing with AQAP (Al-Qaeda in the Arabian Peninsula) is certainly my primary concern."
Asked if Washington still supports Saleh, the defence chief declined to discuss "internal affairs in Yemen."
But a top EU official predicted that the end of Saleh's autocratic rule was now in sight.
"I think that it won't last very long like this," Hugues Mingarelli, head of the European External Action Service's Middle East office, told a European Parliament committee.
"I don't see how the president can hold on much longer, given the fact that part of the army, part of the tribal chiefs and part of his political allies have distanced themselves from him," Mingarelli said.
On Monday, France became the first Western country to openly demand Saleh's departure, saying it was "unavoidable."
Thirteen Al-Qaeda militants were killed in clashes on Tuesday with Yemeni soldiers in Loder, a town in the southern province of Abyan, a stronghold of the radical network, a local official said.
The two sides traded fire with "artillery and machine guns and rocket-propelled grenades," according to a security source.
Against the background of tanks on the streets, Saleh, a key US ally in its "war on terror," warned in an address to his top brass: "Any attempt to reach power via a coup will lead to a civil war in the country."
Medics and witnesses said two soldiers died in a clash near a presidential palace on Monday between the regular army and the Republican Guard, an elite force loyal to Saleh, in the southeastern city of Mukallah.
Defections continued on Tuesday, as soldiers and regime officials announced their support for the "youth revolution" at the square near Sanaa University where protesters have kept vigil since February 21.
Apart from the political crisis and challenge from AQAP, Saleh's government is also faced with an on-off Shiite rebellion in the north and secessionist unrest in the south.
Gates on Tuesday stressed the threat posed beyond its borders by Al-Qaeda's branch in Yemen, the ancestral homeland of Osama bin Laden and where vast areas lie outside central government control even in normal times.
"We consider Al-Qaeda in the Arabian Peninsula, which is largely located in Yemen, to be perhaps the most dangerous of all the franchises of Al-Qaeda right now," the US defence chief said.
AQAP is accused of having masterminded a botched Christmas Day 2009 attempt to blow up a US-bound passenger plane, allegedly carried out by a young Nigerian who reportedly studied in Yemen.
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