William, who is representing the Queen, marks the centenary of what became known as the darkest day of the war for the New Zealand Division, which suffered heavy loses on October 12 1917.
Another 2000 were wounded or taken prisoner.
Speaking at a centenary service commemorating the actions, valour and commitment of the Kiwis, William said newsreels may have described them as ordinary men and women but "there was nothing ordinary about their service or their sacrifice".
"Half a world away, news of the losses was felt like a shockwave".
At Tyne Cot cemetery near the town of Ypres in Flanders, the Duke was welcomed by representatives of the New Zealand government and the Commonwealth War Graves Commission, which has responsibility for the burial space.
"We owe it to the memory of the thousands of New Zealanders who died under horrendous conditions on the Western Front in places like Passchendaele to value the freedom, liberty and justice they fought for and to constantly strive for peace so as to avoid repeats of such tragic conflicts in future".
"Ka maumahara tonu tatou ki a ratou. But while we may never truly understand, we can remember".
Princess Astrid thanked New Zealanders for their sacrifice when her country was destroyed by war.
Before the service began, William and Astrid were greeted by the Maori cultural group of the New Zealand Defence Force, whose spiritual calls and chants rang out across the white headstones.
A plaque inscribed with the Battle of Passchendaele is in parliament, Mr Carter said, and is a ready reminder of the solemn duty he and his colleagues undertake.
The battle on October 12 proved to be particularly deadly for New Zealand, as they tried to capture Bellevue Spur, battling not only German forces but also the rain-soaked bog of what had once been rich farm fields.
Behind the New Zealand troops weapons misfired when the soft dirt gave way beneath the guns, that killed their own men and failed to break through barbed wire fences. The memorial is dedicated to 35,000 soldiers who died in the Ypres region after August 1917, whose graves are unknown.
There are 198 named New Zealand graves at Tyne Cot Cemetery and 322 unknown graves. The memorial commemorates 1166 New Zealanders.