Interestingly enough, this is not the only time a tree appears in Tuwhare's poetry. In Friend, he writes for the last stanza

Perhaps the tree
will strike fresh roots again:
give soothing shade to a hurt and
troubled world.

That is the most relevant passage involving a tree, but a tree appears in many of his poems.

A tree, in his mind, if you look at that last stanza, gives relief, it soothes. An atomic bomb is almost the exact antithesis of that. It is utter destruction. In this context, when the tree, relief, is told to give up - give in - to the atomic bomb, that says a lot about what he thought.

I myself believe it was a nuclear weapon:

raise them not sharply in supplication
to the bright enhaloed cloud.

If you think about what a mushroom cloud would look like from the inside in that very instant before it incinerates you, it would look like a halo - one would merely see the ring, not the whole "poof".

This is no gallant monsoon’s flash,
no dashing trade wind’s blast.

Flashes/blasts are also associated with the atomic bomb. Now, both of these above could probably be construed into thinking of it as a normal bomb, instead of an atomic bomb, but the real clincher for me is

The fading green of your magic
emanations shall not make pure again
these polluted skies . . . for this
is no ordinary sun.

"these polluted skies" - the atomic bomb was unlike other bombs in that instead of just devastation, it pollutes land for many years. Atomic bombs (and their direct descendants hydrogen bombs) have become many, many times more powerful, and therefore that much more polluting, than the only atomic bombs to be dropped.

Finally "for this / is no ordinary sun" - a famous phrase related to the atomic bomb is "a flash brighter than the sun". I think this all together points fairly clearly towards the poem referencing an atomic bomb.

I myself believe it was a nuclear weapon:

raise them not sharply in supplication
to the bright enhaloed cloud.

If you think about what a mushroom cloud would look like from the inside in that very instant before it incinerates you, it would look like a halo - one would merely see the ring, not the whole "poof".

resilience for this is no mere axe
to blunt nor fire to smother.

Note that this means that this is no ordinary explosion. Many standard bombs/explosions are sort of "fiery" and are like a figurative axe - they cut things down, crumble things. But an atomic bomb is different - it completely incinerates things close to the blast, leaving only a darker mark that was the object's shadow.

This is no gallant monsoon’s flash,
no dashing trade wind’s blast.

Flashes/blasts are also associated with the atomic bomb. Now, both of these above could probably be construed into thinking of it as a normal bomb, instead of an atomic bomb, but the real clincher for me is

The fading green of your magic
emanations shall not make pure again
these polluted skies . . . for this
is no ordinary sun.

"these polluted skies" - the atomic bomb was unlike other bombs in that instead of just devastation, it pollutes land for many years. Atomic bombs (and their direct descendants hydrogen bombs) have become many, many times more powerful, and therefore that much more polluting, than the only atomic bombs to be dropped.

Also, "for this / is no ordinary sun" - a famous phrase related to the atomic bomb is "a flash brighter than the sun".

O tree
in the shadowless mountains
the white plains and
the drab sea floor
your end at last is written.

Here, there's an interesting point to consider. Even after an explosion, you can come back after a little bit, and see growth, rebirth. After a fire, after natural disasters, you can also see rebirth. A scene I like to think of is in Disney's Fantasia - after the volcano erupts, it all comes back.

With an atomic bomb, it doesn't work like that. If you look at the area of the Chernobyl disaster, lifeforms are still being born with mutations. There is a whole forest whose needles have turned red from the radiation. 

I think this all together points fairly clearly towards the poem referencing an atomic bomb.

Another point - "Tree let your arms fall" is repeated in the poem. The symbolism there is that of giving up, giving in. There is nothing resistance can do. There is nothing the tree can do against the power of the atomic bomb. It can resist a fire with thick bark. It can resist a storm with its deep roots. It can resist, even, an explosion. But the sun is no ordinary one, and it must give in. Its end "is at last written".