Indonesian security forces are on high alert after the execution of three Islamic militants for the 2002 Bali bombings that killed 202 people.
There were reports of clashes as hundreds of supporters attended burials in the men's home villages in Java.
Imam Samudra, Amrozi Nurhasyim and Ali Ghufron (Mukhlas) were executed by firing squad shortly after midnight on Saturday.
The three were sentenced to death five years ago after being found guilty of planning twin attacks on nightclubs at the resort of Kuta, popular with Western tourists.
The attacks in Bali on 12 October, 2002, killed 202 people, including 88 Australians, 38 Indonesians, 26 Britons and three New Zealanders in the Sari Club and Paddy's Bar.
Hundreds more were wounded.
Security forces are on alert across the country amid fears of reprisal attacks.
A BBC correspondent says the executions took place in darkness surrounded by forest and a handful of witnesses.
Prison officials said an autopsy had been carried out, and Haji Chozin, the brother of Amrozi and Mukhlas, confirmed the deaths.
After being washed by their families, the bodies of Mukhlas and Amrozi were flown by helicopter to their home village of Tenggulan in East Java for burial.
Samudra's body was flown to Serang in West Java.
Members of radical groups gathered, along with onlookers, in both villages to meet the bodies as they arrived.
Some shook their fists in the air chanting "Allahu akbar", although many appeared to be just curious spectators.
Australia to push for end to death penalty
Australia will press for an international moratorium on capital punishment following the execution of the Bali bombers.
Foreign Minister Stephen Smith said on Sunday he had nothing but contempt for the bombers, but Australia did not support the death penalty.
He told ABC Television Australia would in the near future co-sponsor a resolution in the United Nations General Assembly calling for a moratorium on capital punishment.
He said there was a bipartisan opposition to capital punishment in Australia, at the state and federal levels.
But he said Sunday was a sad day for Australia and particularly for the victims' families.
However, he said the executions would bring closure to some of the victims' families.
He also reiterated a warning, issued on Saturday, that Australians should reconsider travelling to Indonesia saying there is "credible information that terrorists may be planning attacks in Indonesia."
Mr Smith urged Australian tourists to avoid beaches, bars and malls in Indonesia.
Notifications to NZ travellers
New Zealanders registered as travelling in Indonesia will be notified that the executions have taken place.
The Ministry of Foreign Affairs advises against all travel to central Sulawesi, and against non-essential travel to Bali and other parts of Indonesia.