"This should have been our starting point when considering publishing the cartoon. That it was not was a deeply regrettable error in judgement.
"We will review our selection process. It must be robust. Our community expects no less."
Before the apology, well-known journalist and TVNZ's Breakfast Host John Campbell shared his disgust over the "shameful" cartoon.
"This is terrible, ODT. What a shameful assault on the cartoonist's art - and on empathy, decency, human feeling, and the people of a country with which we're so close," he wrote.
"As Sita says, most of the 55 lives lost have been under 5. Who would draw this? Who would publish this? And why?"
Sonny Bill Williams tweeted: "Prayers for our Samoan children," in reaction to the cartoon.
Another cartoonist who often works with the Spinoff also shared his outrage.
"Tremain is dragging you down @odtnews. Don't know if it's stubbornness or genuinely the world has passed him by but his total lack of perspective and empathy is rotten. It's outdated and nasty and stinks of childish self-centredness and assumed superiority. Yuck," he wrote
Media commentator Russell Brown said the ODT should fire the cartoonist.
Other Kiwis also shared their disappointment and outrage on Twitter.
