Australian Foreign Minister Alexander Downer has urged a rebel leader in East Timor to surrender to the authorities.
Major Reinado has vowed to fight to the death if necessary
Australian troops are closing in on Major Alfredo Reinado and his men at their hideout in Same, 50km (30 miles) south of the capital Dili.
Maj Reinado said he might negotiate, but added that he would rather die than be made to surrender by force.
The Timorese authorities are pursuing Maj Reinado for his role in clashes with government forces last May.
He was jailed over his role in the unrest, but escaped in a mass breakout from a Dili prison last August.
"It's of concern to us that Reinado is still on the loose, and I think he, appropriately, should surrender himself to the East Timorese authorities," Mr Downer told reporters on Thursday.
Local UN head Atul Khare also told the Associated Press that he wanted Maj Reinado to hand himself in.
Earlier this week East Timor's President Xanana Gusmao said he had authorised Australian-led international forces to track down Reinado, and he accused the rebel soldier of leading a raid on a police post over the weekend.
There are signals that Reinado may be prepared to negotiate with the authorities.
"He has sent a message to the general prosecutor and presidential staff... that this current situation be settled through dialogue and negotiations," East Timor lawmaker Leandro Isaac, who is with Reinado, told the French news agency AFP by telephone.
But he added that Maj Reinado was still vowing to fight to the death if necessary.
Brigadier General Mal Rerden, the Australian in charge of the international peacekeeping force in East Timor, told reporters that it was up to Reinado what happened next.
"If he cares about the people of Timor-Leste, if he cares about the people with him now, he would give up his weapons and surrender," he said.
"Anything that happens from now on is his responsibility."