A national congress of the ruling Fretilin party is under way in Dili and the leadership challenge will come down to a vote by members on Friday.
Members are divided into two camps - those who support Mari Alkatiri and those who want a new Fretilin leader and ultimately a change of government.
Mr Alkatiri's opponent is East Timor's Ambassador to the United States and United Nations Jose Luis Guterres.
The vote was to have been a secret ballot.
However, Fretilin officials aligned with the prime minister have sought to conduct it by an open show of hands.
Mr Guterres says it is a clear attempt to weaken his chances by discouraging delegates to vote for change.
"It's an organised move by the other side in order to strengthen their position," he said.
The final rules of the ballot should be known later in the day.
Mr Alkatiri has pledged to resign as prime minister if he loses the ballot.
Some party members have accused the prime minister of mishandling a violent protest in Dili last month, which left at least five people dead.
The April 28 riot was the worst unrest in East Timor since it voted for independence from Indonesian rule in 1999.
About 50 armed police are guarding a sports complex in Dili, where the Fretilin meeting is taking place.
Tensions are high in the capital, with fears the leadership question could provoke more violence on the streets.
Thousands of residents, who fled the city following last month's unrest, are still too scared to return.