Crowds have been calling for Alkatiri to go
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East Timor's Prime Minister, Mari Alkatiri, has said he is prepared to resign if asked to do so by his party.
Representatives of the governing Fretilin party are gathering in the capital, Dili, to discuss his future.
The meeting was originally planned for Saturday but had to be postponed because of demonstrations against him.
Mr Alkatiri has been engaged in a power struggle with President Xanana Gusmao, who at one stage was threatening to resign unless Mr Alkatiri stood down.
Almost 30 people have died since March in a wave of violence and political chaos after Mr Alkatiri dismissed hundreds of members of the armed forces.
Mr Alkatiri told the Portuguese news agency Lusa on Saturday he was ready to resign if that would lead to "avoiding a bloodbath".
Presidential re-think
Last week, Mr Gusmao sent a letter to Mr Alkatiri demanding he step down in the wake of East Timor's worst violence since independence in 1999.
Gusmao has rethought his threat to resign
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If the prime minister didn't resign, Mr Gusmao said he might do so himself. But a rally on Friday called on the president not to step down.
Mr Gusmao is a widely respected former guerrilla leader, seen as perhaps the only unifying figure amongst East Timor's leaders.
But Mr Alkatiri has become increasingly unpopular. Many people have blamed him for failing to prevent recent unrest which has led to thousands fleeing their homes.
He has also been hit by allegations that he helped recruit a "hit squad" to act against his political opponents - accusations he denies but which Mr Gusmao said contributed to his loss of confidence in his prime minister.
There now a number of armed factions, some originating in the army and police, who are backing one side or the other, says the BBC's Jonathan Head.
In these conditions the United Nations must somehow try to start a new mission to help rebuild the country's damaged institutions.
The prospects for success look unpromising at the moment, our correspondent says.