The governor of Warduk told her the Afghan man who was killed, Younus Khan, was innocent, as were nine others who were injured.
Retiring MP Keith Locke said the claims showed the need for a "thorough inquiry" into the circumstances surrounding Mr Smith's death.
"We are all mourning the death of Lance Corporal Smith, and it would be even more tragic if he died needlessly in a raid motivated by false intelligence.
"A full inquiry needs to be undertaken urgently on the Wardak raid and the public informed of its conclusions."
Mr Locke said the raid showed the SAS were going beyond their mission of providing mentoring for the Afghan Crisis Response Unit.
"It is damaging for New Zealand's reputation if our troops are involved in operations where innocent Afghan civilians are killed."
Former Afghan foreign minister Najibullah Lafraie yesterday said reports of the operation where Mr Smith was killed were "disturbing".
"The team seem to have been engaged in a night raid, similar to the ones carried out by the Americans, and focused upon in the past two years. Hundreds of innocent people have been killed or detained in such operations."
He said the latest death showed that SAS troops were not needed in the region.
The SAS were contributing to instability in Afghanistan by carrying out violent military action, according to Dr Lafraie.
"They don't make any positive contribution.
"I don't think there is a military solution to the problem in Afghanistan. I believe NATO forces have become part of the problem and cannot be part of the solution."
Defence minister visits family
Meanwhile, Defence Minister Wayne Mapp has visited the family of Lance Corporal Smith.
The 33-year-old was single with no children, and left behind his mother, grandmother and two brothers in Wellington, and his father and grandparents in Tauranga.
Dr Mapp, along with Defence Force chief Lieutenant General Rhys Jones, this morning visited the family in Wellington.
Further details about Lance Corporal Smith were released yesterday, including that he was the first person to treat fellow comrade Corporal Doug Grant, who was killed in an attack by the Taliban at the British Council offices in Kabul last month.
Dr Mapp said plans to bring the body home were still underway, but it was expected to happen in the middle of next week.
"That will depend on a lot of variables about availability of flights out of Afghanistan and then back to New Zealand, and how the family wishes that to go,'' Dr Mapp said.