Indonesian immigration and navy officials were trying to negotiate with the migrants who were intercepted off the Indonesian coast on Sunday as they headed to Australia in a wooden cargo boat.
Local immigration chief Harry Purwanto told AFP the boat was divided between those who wanted to accept temporary accommodation and go through the normal refugee applications, and those who favoured continuing the standoff.
Only the men on the boat -- about 150 people -- are refusing food and two of them had been taken to hospital with symptoms resembling dehydration, a port official said.
A spokesman for the group, who calls himself Alex, said: "We are very weak and we don't know how long we can survive like this.
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Asked by mobile phone to explain the migrants' situation, he told AFP he would only speak to "live TV or live radio".
"We are on hunger strike and we need to save as much energy as we can," he said.
Alex earlier threatened to set fire to the boat with cooking utensils.