New Zealand Police has apologised for an "wrong and insensitive" tweet about road crash fatalities.

The tweet posted on the force's Twitter account said "when we have to tell someone their family member has died in a crash," and was accompanied with a gif featuring American Office star Steve Carell.

"This is the worst," read the gif's subtitle

The tweet quickly drew criticism on social media with many branding it ill-judged and distasteful.

One user, Nik Durga, labelled the post "tone-deaf" and the "social media fail of the week".

The offensive tweet was later deleted and an apology issued.

But the apology failed to appease some users, with one insisting it was "staggering" the tweet was sent in the first place.

The force's deputy chief executive public affairs, Karen Jones, said it is "extremely sorry" and would learn from the "mistake".

"We feel terrible about this mistake, as we put victims at the heart of what police do.

"Social media is a hugely important channel to NZ Police and we appreciated the prompt feedback we got from members of our community who pointed out the inappropriateness of the tweet."

"We are extremely sorry and will learn from this," she added.