Married father-of-five Abdulrahman Ikhtiari, 39, originally from Afghanistan, died where he was stabbed on Worcester St in central Christchurch shortly after midnight.
He had one stab wound in the chest and several other smaller wounds, said Detective Senior Sergeant Mike Johnson.
He was found lying dead near his taxi about 1am and witnesses told police they had seen two men running from the scene.
Mr Johnson said the killers would now be "anxious" and would be talking a lot about Mr Ikhtiari's death and asking what people thought about it.
Anyone who witnessed the attack or has information about the two men seen running away should contact police, he said.
The two men were described as in their mid-20s, about 1.8m tall, both with dark skin, of medium athletic build with short dark hair. One man was wearing a white bandanna or cap and dark clothing, and the other was wearing a white top and dark trousers.
Mr Ikhtiari was believed to be one of the Tampa refugees allowed to settle in New Zealand.
Over 400 Afghan refugees were rescued from a sinking Indonesian fishing boat off the Australian coast by a Norwegian container ship, the Tampa, in August 2001.
In the controversy that followed, the Australian government refused to allow the refugees into Australia and they were taken to Nauru.
About 140 of them were later allowed to move to New Zealand.
Mr Ikhtiari was reported to have arrived in New Zealand in May 2002.
