Australia is to pressure Indonesia to rein in the radical Islamic group suspected of involvement in deadly bomb attacks on the holiday island of Bali.
Indonesia is the world's most populous Muslim nation
Prime Minister John Howard said his Foreign Minister Alexander Downer would travel to Jakarta soon to discuss the issue of Jemaah Islamiah (JI).
But Indonesian officials said banning an underground movement was impossible.
Bali marked the major Hindu holiday of Galungan on Wednesday, which celebrates the victory of good over evil.
Mr Howard said that Mr Downer would debate JI's role with the Indonesian government. JI was linked to the 2002 Bali bombs, and blasts this weekend that killed 22, including three suicide bombers.
The Australian prime minister said that simply banning the group, which might not make a difference in practice, may not be the answer, but said he did want the authorities to clamp down on the group's activities.
"[Banning JI] is not the be all and end all of tackling terrorism in Indonesia, and if it remains as it is or if it is banned, in practical terms it's not going to make an enormous difference.
"The real issue is the determination of the Indonesian police and security authorities and government to crack down on the terrorist organisations, their activities rather than their structures," he said.
He also stressed that Australia was not preparing to mount a campaign to change Indonesian law.
"We are having a debate, a discussion about the laws of another country," Mr Howard said. "The Government can't change the laws of Indonesia. We can only put a point of view [across]."
The Indonesian government appeared to rule out an outright ban on the organisation.
"It is an underground movement. We can only ban an established organisation," presidential spokesman Andi Malarangeng told the Associated Press news agency.
President Susilo Bambang Yudhoyono on Wednesday called on the country's armed forces to take a more prominent role in preventing future attacks.
"The terrorist acts have spoiled Indonesia's reputation in the eyes of the world," Mr Yudhoyono said during a speech marking the 60th anniversary of the genesis of the country's military.
The Indonesian police are continuing with their hunt for the bombers' identities.
They told the French news agency AFP that they were seeking five men who had been under surveillance in western Java for their suspected role in previous bombings, including the 2002 Bali attack, and who have apparently disappeared.
"We learned after the Bali bombings that they have not been seen in their areas. Our job is to investigate whether they have links with the Bali bombings," said the police chief in Banten province, Badrodin Haiti.
The people of Bali, meanwhile, continue to mourn.
Dozens visited the site of Saturday's blasts, dressed in traditional clothing, on their way to temples to offer prayers for Galungan.
"I look for blessings so that the spirits are gone," Ketut Arini, 20, a waitress at one of the cafes targeted told Reuters news agency.
Three bombs exploded on Saturday in the tourist areas of Jimbaran and Kuta within moments of each other.
Most of those killed were Indonesian, but casualties are also believed to include people from Australia, Japan, South Korea and the US.
Bali offers an attractive target for JI because it is full of Western tourists in a predominantly Muslim country, says the BBC's security correspondent Frank Gardener.