"We believe one of the suicide bombers studied in the UK and maybe, later on, did his post-graduate (degree) in Australia before coming back to settle in Sri Lanka," he said.
Minister Wijewardene said the investigation has so far revealed that many of the suspects "are well-educated and come from upper middle class and so they are financially independent".
It is understood Prime Minister Scott Morrison and Opposition Leader Bill Shorten will be briefed by security agencies on the development.
Labor frontbencher Mark Butler said the revelation that one of the bombers had studied in Australia was a "really disturbing development".
"A very disturbing development in a really tragic story," he told ABC TV on Wednesday.
"All of us have been deeply touched by what happened on Easter Sunday."
Foreign links probed
Minister Ruwan Wijewardene said the extent of the bombers' foreign links are still being investigated.
"We are looking to all countries neighbouring ours for links to those countries for radicalisation. We are in touch with our counterparts in neighbouring countries and they are assisting us."
Authorities were urgently investigating a claim by the Islamic State group that it staged what was one of the worst militant strikes on civilians in Asia.
Authorities in Colombo have already pointed the finger at a little-known local Islamic extremist group called National Thowheeth Jama'ath (NTJ), but said they were investigating whether they had international support.
Sri Lanka government stands by claim of Christchurch link
Mr Wijewardene said he still stands by claims that the Christchurch attacks inspired the Easter Sunday bombings.
"I think what happened in New Zealand motivated what happened on Easter Sunday," he said, saying his claim is based on an assessment from the country's intelligence agency.
"This is according to an assessment done by intelligence. They believe it is motivated by the Christchurch incident."
New Zealand Prime Minister Jacinda Ardern said on Wednesday her government was not aware of any intelligence suggesting the Sri Lanka attacks were in retaliation for the Christchurch mosque attacks that killed 50 people.
Politicians admit to security lapse, sackings ordered
Officials are investigating why more precautions were not taken after an April 11 warning from Sri Lanka's police that a "foreign intelligence agency" had reported the NTJ was planning suicide attacks on churches.
Government spokesman Rajitha Senaratne said the warning was not passed on to Wickremesinghe or other top ministers.
Defence Minister Ruwan Wijewardene admitted there had been a lapse in security arrangements and intelligence gathering.
President Maithripala Sirisena said late Tuesday he would carry out a complete reorganisation of security forces and police.
"I hope to make major changes in the leadership of the security forces in the next 24 hours," Sirisena said in a nationwide address.
Sri Lanka's police chief issued a warning on April 11 that NTJ suicide bombings were possible and alerts had been given by a foreign intelligence agency.
Wickremesinghe has acknowledged that the information was not passed to his office or other top ministers.
CNN reported that Indian intelligence services had passed on "unusually specific" information in the weeks before the attacks, and that at least some of it came from an IS suspect in their custody.
Sri Lankan Muslim leaders said they have also made many complaints to police about Hashim's activities in recent months. His whereabouts after the bombings were unknown.
Death toll rises to 359
Police spokesman Ruwan Gunasekera said the death toll had risen to 359 from 321, with about 500 people wounded, but did not give a breakdown of casualties from the three churches and four hotels hit by the bombers.
Mourners have gathered for the first of the funerals, including a service for Australian Manik Suriaaratchi and her 10-year-old daughter, Alexendria, who were laid to rest near Ms Suriaaratchi childhood village, according to the ABC.
Work was continuing to identify foreign victims in the blasts.
A Danish billionaire lost three of his children in the attacks, a spokesman for his company said.
Eight Britons, 10 Indians, four Americans and nationals from Turkey, Australia, Japan and Portugal were also reported killed.
The United Nations said at least 45 children, Sri Lankans and foreigners, were among those who lost their lives.
Of the three churches targeted, two are in the Colombo region and one is in the eastern city of Batticaloa.
The Easter Sunday bombings shattered the relative calm that has existed in Buddhist-majority Sri Lanka since a civil war against mostly Hindu, ethnic Tamil separatists ended 10 years ago, and raised fears of a return to sectarian violence.
Sri Lanka’s 22 million people include minority Christians, Muslims and Hindus. Until now, Christians had largely managed to avoid the worst of the island’s conflict and communal tensions.