Members of the NZ Provincial Reconstruction Team were joined at the ramp ceremony by coalition allies, including US Chairman of the Joint Chiefs of Staff, General Martin E. Dempsey, Commander International Security Assistance Force (ISAF), General John Allen and Deputy Commanding General, US Forces - Afghanistan, Lieutenant General James Terry.
Defence Force chief Lieutenant General Rhys Jones said there had been "many offers of support and expressions of condolence from our friends in the wider international military community''.
The three troops were killed on Sunday when a roadside bomb destroyed their Humvee in Bamiyan province.
New Zealand's military toll in Afghanistan stands at 10.
The Taleban has claimed responsibility for the rocket attack on the Bagram Air Field overnight.
A rocket hit the C-17 military transport plane of US Army General Martin Dempsey, who was in Afghanistan to discuss the state of the 10-year-old war, AP reported.
Senior military adviser to the NZ Provincial Reconstruction Team, Lieutenant Colonel Pete Hall, released the following statement:
"Luke, Jacinda and Richard epitomised the values that we hold dearest and always hope we can live up to - those of courage, commitment, comradeship and integrity.
"They were killed whilst undertaking a righteous and honourable endeavour assisting the people of Afghanistan to build a better place for the future - commitment;
"They deployed to a country in turmoil knowing that their lives would be at risk, but still they came - courage;
"They survived the Battle of Baghak where they fought honourably and bravely alongside their mates, tended the wounds of those that required care and arranged for their safe evacuation - comradeship;
"They set the example for our Afghan partners on how to perform their duties in a professional and honest way and by their example helped to develop their skills - integrity.
"Luke, Jacinda and Richard's lives were cut short by a cowardly act (I take some solace in the fact that they died instantly with no pain).
They shall grow not old as we that are left grow old
Age shall not weary them
Nor the years condemn
At the going down of the sun and in the morning we will remember them.
"They are forever in our hearts. They will never be forgotten.
"I think of their families everyday, I am heartbroken for their loss and can offer little comfort other than to assure them that in honour of their memory we, the members of CRIB 20, will complete our task applying the values that Luke, Jacinda and Richard lived by.
"I am a better man for having known them.
"Prepare the way my brothers and sister in arms for the rest of us to follow, like those of us that remain behind, you will always be part of CRIB 20, and we will surely meet again.''
