The chief police investigator said Imam Samudra, who is alleged to have links with Islamic militant group Jemaah Islamiah (JI), led both the planning and the execution of the attacks on the Sari Club and Paddy's Bar.
Police said details of the suspects emerged from the interrogation of an Indonesian man named Amrozi - the only person who has so far been arrested in connection with the bombings.
Nearly 200 people were killed in the attacks.
At an hour-long news conference on Sunday, police told how Samudra - described as wearing a hat and often carrying a laptop computer case - remained in Bali for four days after the blast observing the police investigations.
"He is also a suspect for the Christmas bombing in Riau, Batam and Jakarta," Major General I Made Mangku Pastika said, referring to a string of attacks in 2000.
Police say they now have a detailed picture of how the bombings were planned and carried out, and the various roles of the suspects.
He said all the suspects were still thought to be in Indonesia and would be arrested "as soon as possible".
But the BBC's Jonathan Head in Jakarta says there is a good chance that the suspects may not be apprehended, as the Indonesian police are thinly stretched.
Bomb-maker
Indonesian officials have previously identified Imam Samudra as one of the leaders of JI.
But investigators had not linked the bombing to JI, or to the al-Qaeda network with which it is thought to be affiliated.
Major General Pastika said Samudra, a native of Sunda on Java island, had frequently visited Afghanistan and learned to make bombs there.
The revelations come after Indonesian police faced strong criticism for carrying out an hour-long public interrogation of a giggling and gloating Amrozi before journalists on Wednesday.
Correspondents say the spectacle only served to erode the credibility of the investigation, while incensing Australians who bore the brunt of the deaths among foreign tourists.
On Friday, Australian Prime Minister John Howard ordered an inquiry into a claim that Australia was warned about the attack just before the bombings.