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New Zealand's parliamentary Speaker Trevor Mallard said Anzac Cove continued to have a special place "in the hearts of all of us".
"And it informs our rejection of extremism and of terrorism, whether it occurs in Turkey, in Australia, in New Zealand or in Sri Lanka," he told the service.
The arrest didn't deter some 1100 Australians and Kiwis who attended the service at Anzac Cove.
"I feel quite safe, I feel that if there is any concerns, that it would have been called off and they wouldn't have put us at risk," said Chris King, a nurse from New Zealand.
Speaking in Australia before the service began in Turkey, Prime Minister Scott Morrison said there was no clear link between the arrest by Turkish police and any Anzac Day event at Gallipoli.
"This is more of a routine thing that we've seen happen with Turkish authorities and we could not say at all that there is any link between that arrest and any planned event at Gallipoli," Mr Morrison told reporters in Townsville.
A man - who was believed to be planning a terror attack - was arrested in the Turkish province of Tekirdag, three hours from the Gallipoli peninsula, ahead of the service.
Australian media reported the Syrian national was planning to bomb the service or drive a car into the crowd, in retaliation for the Christchurch mosque attacks. Fifty people died and another 40 were injured after two mosques were targeted on March 15.
Security sources told the ABC the attack was planned in retaliation for Christchurch. Demiroren news agency also said the man was preparing for an attack on the commemorations in retaliation for the attacks on Muslims in mosques in New Zealand.
Every year, Australians and New Zealanders travel to Turkey for memorial services commemorating the failed 1915 military campaign by ANZAC and allied forces to drive Ottoman troops from Gallipoli and the Dardanelles region.
Australia's Chief of the Defence Force Angus Campbell said the story of Gallipoli left an indelible mark in the nations' collective history.
"It is one of our nation's foundational stories, one that means a great deal to a great many people," he said.
In New Zealand, addressing thousands gathered for a Dawn Service at the Auckland War Memorial Museum, Prime Minister Jacinda Ardern said that, in the wake of the Christchurch massacre, Anzac Day 2019 should be an even greater uniting force.
"Let us recommit to always remembering our shared humanity that there is more that unites us than divides us Our sense of independence is as strong as our sense of responsibility to each other and not just as nation states but as human beings. That is part of the Anzac legacy."
On Wednesday, soldiers from New Zealand, Australia, Turkey and other countries held several services on the peninsula. At dawn on Thursday, Australians and New Zealanders are due to hold a special dawn service marking the landings by ANZAC (Australian and New Zealand Army Corps) forces.
Turkey has said Islamic State was responsible for several bombings that took place in 2015 and 2016, which in total killed some 200 people. Although the militant group has not been active in Turkey of late, authorities still carry out routine operations against suspected Islamic State members.
This year's Anzac service comes a month after Turkish President Tayyip Erdogan faced criticism from Australia and New Zealand for comments he made after a lone gunman attacked the Christchurch mosques.
Erdogan played a video from the shootings at local election rallies and said the gunman had targeted Turkey by saying in a manifesto posted online that Turks should be removed from the European half of Istanbul. He also threatened to send back in coffins anyone who tried to take the battle to Istanbul.