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Nicholas Heyward was shot dead in the city of Mendoza during a robbery.
Police released a man arrested yesterday, but have since arrested two others.
One who'd bragged about the shooting and the other - who was with him - because he had a weapon.
One of the men arrested over the killing of a New Zealander in Argentina matches a police sketch - but witnesses say he's not the man they saw in the fatal robbery.
Correspondent Jayson McNamara told Newstalk ZB he can't say if the two arrested are known criminals, but does have some details of the shooter.
"He's a 19-year-old male who fits the description that was established by the police sketch.
he had shaved head down the sides and a bit of a mohawk.''
McNamara says the other arrested man was with the first and carrying a weapon.
Police are keen to get the case out of the international spotlight.
"I would imagine they'll be keeping the same level of intensity with this case throughout the coming days. They really want to solve it as soon as possible,'' adds McNamara
Friend relives Kiwi's killing
A friend who was with Nicholas Heyward when he was killed by motorcycle bandits in an Argentine park has told how the fatal chain of events unfolded - and how she tried to treat his injuries.
Fiona Darling, a 34-year-old Australian, was walking with Mr Heyward and Frenchman Pierre D'Amico when two men on a motorbike approached. One was brandishing a gun and yelling "Give us your camera" to Mr Heyward.
He did everything he could to oblige but the bag strapped across his body got stuck when he went to take it off, Ms Darling said.
As the New Zealander was trying to hand it over, the passenger got off the bike, shot at the ground and lurched towards Mr Heyward who was frozen with shock. Ms Darling and Mr D'Amico, 29, ran at the sight of the gun.
Ms Darling gave her account of the incident to police in Mendoza.
Veronica Albornoz, an officer who works in the police tourist unit, said Ms Darling saw the gunman and Mr Heyward start fighting - then she heard more shots.
"When she turned back, she saw Nick fall to the ground," Mrs Albornoz told the Herald.
Mr Heyward was shot in the right side of his neck, in his chest and twice in his pelvis with a .22-calibre pistol. Ms Darling and Mr D'Amico tried to save their friend who was still conscious in the moments after the attack.
Ms Darling rolled her friend on to his back, performed CPR and tried to stop the heavy bleeding from Mr Heyward's neck. But his injuries were too serious and he had lost too much blood and he passed away within minutes of the attack at 3.40pm on Monday, Argentina time.
Mrs Albornoz has been supporting Mr Heyward's friends and said both were still in shock.
Mr D'Amico met Mr Heyward two months ago in El Chalten, in Argentina's southern Patagonia region, and had been travelling the country with him. Three weeks ago, in Bariloche, about 1300km south of Mendoza, they met Ms Darling.
Mrs Albornoz said Mr D'Amico, who speaks Spanish, spent hours with a police sketch artist to create an image of one of the attackers who wasn't wearing a helmet.
Police are under pressure to find the killers quickly because Mr Heyward's friends are leaving the country today.
It is understood Mr Heyward's brother is travelling to Mendoza to collect his body and take it back to Australia, where most of his family live. Meanwhile, Security Minister Leonardo Comperatore has offered his resignation following the death.
The grandparents of Nicholas Heyward are considering whether they will be able to travel to Australia for his funeral.
Hugh Nees last night told the Herald from his Paraparaumu home that they were debating whether the trip was realistic.
Mr Nees, 93, said he was not sure if he was capable of the journey, and his wife Joan, 91, had suffered ill-health recently.
"She'd very much like to go. I think we are trying to work out whether she is fit enough to do it. There's nothing definite about that yet."
He expected the funeral to be held next weekend, although no date had been settled as arrangements were still being made.
Mr Heyward's mother, Margaret Nees, died in a car crash when he was younger. He travelled on a New Zealand passport but lived in Australia with his father and brothers.
He visited his New Zealand grandparents last year before a period of overseas travel.