The answer to this is that Kivi is the one who appears when Mafatu is ready to die bravely like Uri.  Kivi is an albatross.  We find out early in the book (p. 13 in my edition) that Mafatu found Kivi when it was still a young bird.  Kivi was being picked on for having one foot much smaller than the other.  Mafatu identified with the bird and saved it. 

The incident that you ask about in this question occurs on pages 29 and 30.  Mafatu has left Hikueru to prove himself.  He has been in the canoe some days without any rain and he and Uri are about to die.  They lost all of their provisions in the storm.  Mafatu is touched by Uri’s ability to still wag his tail even though he is about to die.  This gives him new strength.  Then Kivi appears.  We are told that

In that instant he heard a whir and a fury in the sky above… 

He looks up, and sees Kivi.  Kivi’s flight path shows Mafatu that an island is near.  Thus, Kivi encourages Mafatu not to give up and shows him where the land is.