DILI (BBC) -- Thousands of people have gathered in East Timor's capital, Dili, to support President Xanana Gusmao in his battle of wills against Premier Mari Alkatiri.

On Thursday Gusmao demanded that Alkatiri step down, following weeks of street violence in Dili.

He said that if Alkatiri refused to go, he would leave office himself.

There are signs, though, that the president may reconsider this threat. After meeting him, a senior bishop said he had "agreed to rethink".

Bishop Alberto Ricardo da Silva, whose church has a great influence on largely Roman Catholic East Timor, said the president had promised to consider his options.

About 2,000 protesters gathered outside Dili's government house on Friday, to demand that Alkatiri resign rather than Mr. Gusmao.

Gusmao threatened to step down himself on Thursday. "The president should not step down," one of the protest organizers, Agosto Junio, told AFP news agency. "Mari Alkatiri is the one to blame for the trouble. He is a communist, a criminal."

Security was tight around the protesters, with foreign peacekeepers helping local police to keep control.

The peacekeepers were drafted into East Timor to quell the escalating street battles that killed at least 21 people and caused thousands more to flee to refugee camps.

It was Alkatiri's decision to sack 600 soldiers in March which sparked the unrest, and critics say he should resign to take responsibility for what happened.

He has also been accused of recruiting a group of former fighters to act against his political opponents - allegations which, although unproven, have increased the calls for him to stand down.

Gusmao added his weight to those calls on Thursday, saying in a televised address that the ruling party, Fretilin, had to make a decision.

"Fretilin has to choose, ask Mari Alkatiri to take responsibility for the major crisis .... or tomorrow, I will send a letter to Parliament to inform them that I will resign from being president of the republic, because I am ashamed of all the bad things that have happened," he said.

Fretilin did make a choice, but not the one Gusmao wanted.

After a meeting to discuss the issue on Thursday, Fretilin said that Mr. Alkatiri had been "reaffirmed" as prime minister.

Alkatiri also repeated that he would not resign, telling the Portuguese news agency Lusa that "a hasty decision could further complicate things".

The rivalry between the two men has been simmering for years, but now it appears to be out in the open.

The president is a widely respected former guerrilla leader, revered for his role in helping East Timor achieve independence from Indonesia.

Alkatiri, a veteran of East Timor's independence movement, is credited with skillfully negotiating with Australia over East Timor's rights to oilfields in the Timor Sea, but is also viewed by many Timorese as a cold and arrogant politician.