About 500 people reportedly turned out on the streets of Dili, East Timor's capital, on Monday, to protest against the raid on Reinado's hideout.
Many chanted slogans against Gusmao, who ordered the raid by a largely Australian-manned security force.
Fear of violence
With East Timor scheduled to hold presidential elections next month, Australian and UN security officials have said they fear more widespread violence will break out if the rebel leader is killed or injured by Australian troops.
Reinado was jailed last year for leading a mutiny with nearly 600 soldiers and deserting East Timor's armed forces.
"I will not surrender for the president and prime minister's interest. I will surrender only for the peoples' interest"
Alfredo Reinado, rebel leader
The mutiny triggered clashes between rival factions of the security forces and led to the worst violence seen in East Timor since its bloody break from Indonesia in 1999.
He escaped from prison in September along with 50 other inmates.
Saturday's raid on his hideout followed accusations that Reinado and his followers had attacked a police post last month, stealing a cache of automatic weapons.
After the raid, Gusmao urged Reinado to surrender, saying the government would treat him with respect.
Reinado is being pursued by security forces in helicopters and by foot patrols around the town of Same, about 50km south of Dili.
Australian urgesReinado has said he will not surrender to international troops.
"I will only surrender to the law, not to any international power," Reinado told Reuters on Saturday.
"I will not surrender for the president and prime minister's interest. I will surrender only for the peoples' interest."
|A mutiny led by Reinado, left, last year |
caused clashes between rival factions [EPA]
The Australian government, which has around 800 troops providing security in East Timor, has also urged Reinado to give himself up.
John Howard, the Australian prime minister, said Reinado and his followers were "a threat to the security of East Timor, and it is preferable that that threat be neutralised".
"Our objective is very clear. We prefer taking people into custody and we are hopeful that objective will be achieved," Howard said in a television interview on Monday.
"But he is a fugitive. He did escape, and he does have people around him."