Council buses will be operating from Helensville to Glen Eden for an Anzac Day service, however, the exact details are yet to be confirmed.
The announcement from Coste follows recommendations from Auckland Police on Friday for fewer Anzac Day events to be held throughout the city.
Auckland City district commander Superintendent Karyn Malthus said fewer events would make it easier for officers to ensure the safety of those attending.
She did not have any information to suggest there was a "specific risk" to the safety of the public, however.
"In the current environment, police are continuing to provide a visible presence nationwide for the safety and reassurance of the community," she said.
"We recognise the public will want to commemorate Anzac Day across the region and we are wanting them to do that in the safest way possible, which may mean some have to travel a little further to an event."
In his Facebook post, Coste said he and police had inspected potential locations for the service to be held but they did not meet safety requirements.
The national terror threat level was raised to high following the Christchurch terrorist attacks on March 15 and have not been lowered since.
The Howick RSA had also announced the Anzac Day parades had been cancelled due to security concerns raised by police, but the Dawn and Civic Commemoration Services on Stockade Hill would still proceed at 6.05am and 11am respectively.
Simon Strombom, the organiser of the Tatahi Bay service, planned to have a Muslim cleric say a prayer at the service but received a number of "frightening threats".
He believed the prayer was an opportunity to rise up and become an inclusive nation but due to safety concerns, the prayer was retracted.
"We can't guarantee certain speakers' safety with the amount of comments we've had coming in online which are clearly directed at Muslim hatred.
"After speaking with police and our Muslim community we have decided that including the prayer would be too risky so for security reasons we have decided to cancel the idea."