His daughters, Hanan Khadem Chilab and Wjdan Khadem Chilab, said tearfully he was due to visit New Zealand just two days before his death.
A relative called them early on Saturday morning to say he had been killed. It was Wjdan's 23rd birthday.
"They said to me, your dad's dead. I didn't believe him," Wjdan said. "We opened the army's Facebook page and there were messages saying peace be upon him, he is martyred."
Hanan had been told by relatives that Mr Abbas was driving near an oil refinery when an explosion from a rocket, believed to be fired by Isis fighters, ripped through the car he was in.
"A rocket hit my dad's car. His head exploded - only a small part of him remained."
Their 18-year-old brother, also a soldier, found his father's remains, a piece of him about the size of a forearm.
From their living room in Napier, the sisters cried as they watched video footage of their brother pulling at his clothes in despair.
"The way he died is the thing that broke us down. His head being blown off, I don't think we'll ever be able to handle it."
Her father was a tall, muscular man, but his remains weighed just a few kilograms.
Hanan said the family had feared for Mr Abbas when he left for Iraq.
"He wanted to see his family and protect them, and protect others.
"He was trying to free the land from the Isis terrorists."
The sisters had also lost an uncle and a cousin to Isis forces in December. Their mother was currently in Iraq, overseeing Mr Abbas' burial.
"We are in pain, and half of us may not even live," said Wdjan.
She worried her brothers would try take revenge.
Hanan, a registered nurse and Arabic interpreter, said she did not believe Isis terrorists were Muslims.
"There is no religion that accepts women or children should be killed. Isis have never and will never be part of Islam. They are not Muslims," she said.
Wjdan said her father was a hero: "He died protecting all of us."
Mr Abbas leaves behind 24 children - 12 in Iraq, 12 in New Zealand - including a 5-month-old daughter he had never met.
The Ministry of Foreign Affairs (Mfat) was unable to confirm any details about the incident yesterday, saying it had not been approached by family members.
A spokeswoman said: "Given there is no New Zealand diplomatic presence in Syria or Iraq, the ability of the Government to assist New Zealand citizens requiring consular assistance there is severely limited."
Mfat advised against all travel to both countries.
The family's loss comes after New Zealand-born Karolina Dam, now living in Denmark, revealed this week her son Lukas had been killed after travelling to Syria to fight for the Islamic State.
The Government has urged New Zealanders not to join either side of the conflict in Iraq and Syria. However, while it has spoken of sanctions for "foreign fighters" when they returned to this country, it is not clear whether these penalties would apply to New Zealanders who fought against Isis.
Additional reporting: NZME.
