The President Michael D Higgins has signed a book of condolence for the victims of the Christchurch terror attacks.

He visited the New Zealand embassy in Dublin on Wednesday morning.

At the New Zealand Embassy in Dublin this morning, President Higgins signed a book of condolence for the victims of the Christchurch terror attacks. pic.twitter.com/HXUILI0jjz

— President of Ireland (@PresidentIRL) March 20, 2019

It comes as a father and his teenage son were the first to be buried, as funerals began.

Khalid Mustafa (44) and Hamza Mustafa (15) were Syrian refugees and were murdered last Friday when a man opened fire at two Christchurch mosques.

Younger brother, Zaed (13), watched the service from a wheelchair after being shot in the leg during the attack.

Hundreds of people gathered as mourners carried the bodies up to a freshly-dug Muslim grave site.

New Zealand Prime Minister Jacinda Ardern later told reporters: "I cannot tell you how gutting it is to know that a family came here for safety, for refuge, and they should have been safe here."

School principle Mark Wilson said Hamza was a compassionate and hardworking student, and hoped to become a vet.

The bodies of 30 of the 50 victims have now been approved for release to families, said Ms Ardern, amid frustration from some relatives over the time it has taken.

Muslim burials should take place as soon as possible, preferably within 24 hours.

A memorial service for the victims is also being planned which could involve international representatives, Ms Ardern said.

Woman mourners pray during the funeral of a victim of the mosque shootings at the Memorial Park Cemetery in Christchurch, New Zealand | Image: Mark Baker/AP/Press Association Images

She said there would be a two-minute silence a week on from the attack, and that the Muslim call to prayer would be broadcast on TV and radio.

Ms Ardern also visited the school of two of the victims on Wednesday and met police and ambulance staff.

She told them: "I switched on the television and I saw you... I have no doubt you saved lives. And so to everyone who was part of that response, on behalf of New Zealand, thank you."

She told the media an "extraordinary effort" was under way to quickly bring in tighter gun laws - with the outcome due next week.

The far-right extremist in custody over the attack was able to buy some weapons online and used a semi-automatic weapon in the massacre.

Ms Ardern said New Zealand was "in some ways a blueprint of what not to do" when it comes to gun control.

She said she believed gun owners would back the changes, adding: "There isn't and should not be a place for military-style semi-automatics."

New Zealand's Prime Minister Jacinda Ardern, second from right, arrives during a school visit in Christchurch, New Zealand | Image: Vincent Thian/AP/Press Association Images

Ms Ardern - who has been praised for her response to the attack - simply said "yes" when asked if the terror attack was the hardest thing she has had to deal with.

"I feel the grief but I also have a duty of care to people involved in this to also keep going," she said.

"So if the Imam who stood at the front of a mosque and saw first-hand the loss of his worshippers in front of him can keep going, then I definitely can."

She also refused to be drawn on comments by the Turkish president, who on Tuesday showed clips from the killer's live stream of the attack during a local election event.

President Erdogan used the clip to denounce Islamophobia and criticised New Zealand and Australia for sending troops to Turkey in the First World War, saying there was an anti-Islam motive.

Ms Ardern said her deputy prime minister was heading to Turkey to "directly" confront the issue.

Social media sites have been criticised for not doing enough to stop the video of the attack from spreading, and Ms Ardern said clamping down on material that incites violence would likely need an international response.

Facebook vice president Chris Sonderby said on Wednesday that no one had flagged up the video during its live broadcast, which was viewed 200 times.

He said the company removed 1.5 million copies of the video in the first 24 hours.

An industry group that includes Facebook, YouTube, Microsoft and Twitter has also said it has added more than 800 versions of the video to a database used to block violent terror material.

The Global Internet Forum to Counter Terrorism said users were trying to share the video by editing it or making versions with different "digital fingerprints".

Additional reporting: Jack Quann