Touring the scene of the blast on Friday, Australian Foreign Minister Alexander Downer said police had received a mobile phone text message before the bombing saying that foreign missions in Jakarta would be attacked unless the alleged head of the Jemaah Islamiya (JI) group, Abu Bakr Bashir, was freed.
Bashir is currently in jail awaiting trial on charges that he heads the JI, which police have accused of carrying out Thursday's attack in which nine people died.
The same group is blamed for the 2002 Bali bombings and an attack last year on the JW Marriott Hotel.
Australia and the United States have both publicly accused Bashir of terrorism, and urged Indonesia to prosecute him. Bashir denies any wrongdoing.
Canberra not warned
Thursday's blast shook Jakarta's
The threat claim is a potential cause of friction between the two countries which have seen close cooperation on security following the Bali nightclub bombings.
Indonesian police said they received no prior warning of the attack.
However, Australian Prime Minister John Howard repeated Downer's allegation at a press conference in Canberra, saying the warning was not passed on to Australian Federal Police until hours after Thursday's bombing.
Indonesian officials say the embassy attack bears the hallmarks of JI alleged bombmaker, Malaysian Azahari Husin, wanted along with compatriot Noordin Mohammad Top for the Bali blasts and the Marriott bombing.
Indonesian police may recently have come close to catching Husin.
General Da'i Bachtiar said within the last two months police had raided a house on the outskirts of Jakarta, not far from the international airport, where a group of men wanted over previous bomb attacks had been hiding.
He said that one of the men, based on descriptions given by local residents, could have been Husin, and Top could also have been in the group.
Australia is increasing security in
response to the attack
Howard said there would be a boost in security at home and abroad in response to the attack and possible future attacks.
He faces tough elections on 9 October with his conservative coalition running closely against the opposition Labor party.
Howard announced an immediate series of fresh counter-terrorism steps, including the creation of a 24-hour-a-day Federal Police national operations centre and a Canberra-based emergency response team of 10 officers with access to specialist electronic surveillance technology.
Security is also being upgraded around airports, other transportation and overseas missions considered at risk, he said.
Deputy Prime Minister John Anderson, who is also transport minister, said these measures would include deploying all available explosives detection equipment and sniffer dogs to key transport hubs.
Screening of passengers and baggage travelling between Australia and Indonesia is also being tightened.