Islamic State made the claim of responsibility via its Amaq news agency.

"The perpetrators of the attack that targeted nationals of the countries of the coalitions and Christians in Sri Lanka before yesterday are fighters from the Islamic State," the message said.

The news agency also provided the nom de guerres of the seven suicide bombers in Sri Lanka and an image of what it says were the attackers standing before the ISIS flag, according to Rukmini Callimachi, the New York Times' correspondent covering Islamic State.

Islamic State has made a series of unsupported claims of responsibility for past attacks. Callimachi said it was also very rare for the terrorist group to take two days to claim responsibility for an attack.

Meanwhile, State Minister of Defence Ruwan Wijewardene told a special session of the Sri Lankan Parliament that early investigations indicated the bombings could have been retaliation for the terrorist attacks on two mosques in Christchurch, New Zealand, that killed 50 people last month.

"The initial investigation has revealed that this was in retaliation for the New Zealand mosque attack," Wijewardene told Parliament.

"It was done by National Thowheeth Jamaut along with JMI," he said, referring to another local group, Jammiyathul Millathu Ibrahim.

He also said investigators were also probing links between the little-known local jihadist group National Thowfeek Jamaath (NTJ) and another extremist group known as Jamaat-ul-Mujahideen.

It was not clear whether that group is associated with the Bangladeshi listed terror organisation of the same name.

The office of New Zealand Prime Minister Jacinda Ardern said the country had "not yet seen any intelligence upon which such an assessment might be based". Nor did Wijewardene offer any evidence for the connection.

Terrorism researchers have suggested it could have taken months to plan the coordinated bombings.

A spokesperson for Ardern said: "We have seen reports of the statement from the Sri Lankan minister of state for defence, alleging a link between the the Easter Sunday terrorist attack and the March 15 attack in Christchurch.

"We understand the Sri Lankan investigation into the attack is in its early stages. New Zealand has not yet seen any intelligence upon which such an assessment might be based.

"New Zealanders oppose terrorism and extreme violence in all its forms. In the wake of the Christchurch mosque attacks, it was the condemnation of the perpetrators of violence and a message of peace that unified us all."

Amid mass funerals on Tuesday, attention has turned to obscure groups the island nation's government suspects carried out the coordinated blasts which hit churches and luxury hotels killing at least 321 people, including two Australians.

CCTV was released on Tuesday of a man, dressed casually and with a backpack strapped around his waist, walking calmy into St Sebastian's church.

Cabinet Minister Rajitha Senaratne suggested NTJ had assistance from international militants to stage the attacks.

"We do not believe these attacks were carried out by a group of people who were confined to this country," he said. "There was an international network without which these attacks could not have succeeded."

A Syrian national is in custody and being questioned over the attacks, Reuters reported.

Police said 40 people are now being held following the worst violence in Sri Lanka since the end of the country's three-decade civil war between Tamil separatists and the Sri Lankan army, which ended in 2009.

The NTJ originated around a decade ago on Sri Lanka's east coast and is understood to follow the conservative Salafist form of Islam practised in Saudi Arabia.

It has no previous history of large-scale terrorist attacks although it was last year blamed for defacing Buddhist statues.

The Wall Street Journal reported the group had gained traction with a small number of middle-class and wealthier Muslims in Sri Lanka and that some had left the country to join Islamic State.

Its purported leader, known as Mohammed Zahran or Zahran Hashmi, began posting videos online three years ago calling for non-Muslims to be "eliminated", faith leaders said on Tuesday.

He became known to Muslim leaders three years ago for his incendiary speeches online.

The attacks, described by one Sri Lankan minister as a "colossal failure on the part of the intelligence services", appear to have triggered rifts between key figures in the government.

Late on Sunday, Prime Minister Ranil Wickremesinghe suggested authorities had received warnings but "not enough attention had been paid".

There are reports that both Indian and US intelligence had warned the country about a threat of attack in early April.

Sri Lanka's capital Colombo was tense on Tuesday as the military took on emergency war-time powers, allowing them to conduct searches without a warrant and to detain suspects for up to two weeks before a court hearing. These powers haven't been used since the end of Sri Lanka's civil war.

Wickremesinghe called for national unity as the country marked a day of mourning for victims.

"It is imperative that we remain unified as Sri Lankans in the face of this unspeakable tragedy," he said in a statement posted on Twitter.

Earlier on Tuesday, a mass funeral was held at St Sebastian's Church in Negombo, north of Colombo, where more than 100 people died in one of Sunday's several targeted blasts.

On Tuesday afternoon, Sri Lankan police lifted the death toll from the attacks to 321 with around 500 injured.

SMH/The Age with agencies