Lance Corporal Pralli Durrer and Lance Corporal Rory Malone, both 26-years-old, died on Saturday night (NZT) about half-way through their deployment with the Provincial Reconstruction Team (PRT) in Bamiyan.
Lance Corporal Durrer, who was from Christchurch, had an aunt and grandfather as next-of-kin, as both his parents are dead.
This afternoon, Corporal Durrer's grandfather, Jack declined to comment.
A statement released by the family said they were going through a very difficult time.
"Support we are receiving from our wider family, friends and Pralli's Army family has been encouraging and we are thankful that Pralli will be home with us soon.
"We are thankful for the 26 years we had with Pralli and are proud of all that he accomplished in his short time with us. He has had a rewarding career as a soldier and we know that he had a positive effect on all those he worked alongside throughout his time with the NZ Army,'' the statement said.
Corporal Durrer joined the Army in June 2004 as a rifleman.
In September 2009 his trade was changed to crewman with the Royal New Zealand Armed Corps and he was posted to the Queen Alexandra's Mounted Rifles, then in Burnham in Christchurch.
He had been previously deployed to Timor-Leste in 2006/2007.
Corporal Malone was from Auckland. His mother is separated from his father, and lives overseas.
A brother was listed as Corporal Malone's next-of kin.
A statement from his family said they were very saddened by the loss.
"Rory's family is extremely proud of his service to the NZ Army. Rory went to Afghanistan to do what he considered an important job which contributed to the greater good of the region. He did his job with honour and pride. Rory will be dearly missed by his family.
Corporal Malone joined the Army Reserve Force in November 2002 and transferred to the Regular Force as a rifleman where he was posted to the 2nd/1st Battalion Royal New Zealand Infantry Regiment, based in Burnham.
He had previously been deployed to Timor-Lest in 2006 and again in 2007, and was promoted to Lance Corporal just last month.
Both men were deployed to Afghanistan in April.
Their bodies are now at the Bagram Air Force Base and arrangements are being made to bring them back to New Zealand, Chief of Defence Force Lieutenant General Rhys Jones said.
The bodies were expected to be back in New Zealand by mid-week.
Lance Corporal Malone was shot as he was going to assist a company commander who had been injured, General Jones said.
He was killed instantly.
Lance Corporal Durrer was a crew commander of a light armoured vehicle and was also shot. He died during the evacuation.
At the time of the attack, New Zealand forces were helping the Afghan Special Police who had been ambushed as they went to arrest an improvised explosive device bomb-maker.
Four New Zealand teams were deployed at the site, in the north-east of the Bamiyan Province, south of the township of Do Abe.
Soon after midday (Afghan time) the New Zealand forces moved to higher ground to provide protection for the Afghan police who would start evaluating the operation.
But the troops moving in that area came under attack and both men were killed within the first three minutes of the attack, General Jones said.
A further six New Zealand personal were injured during the battle.
Five of those men were either being transferred to a hospital in Germany, or were about to be transferred.
The sixth man, who was the most seriously injured with a gunshot wound to the neck, would be transferred to Germany when his condition improved.
It was likely that at least three of the men would return to New Zealand.
General Jones said some insurgents were killed in the exchange but it would probably never be known how many.
Last night members of the PRT came under fire from small arms and rocket propelled grenades in the village of Do Abe, General Jones said.
"This was just a show of force to show they [insurgents] are still in the area,'' he said.
The attack ceased within an hour and no one was injured.
"We have begun reviewing this attack, which will feed into our picture of the security challenged in this part of Bamiyan,'' General Jones said.
It was not yet known when funerals for the two men would happen.
The Taliban has claimed responsibility for the initial attack, but the New Zealand Defence Force has yet to confirm that.
