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The Minister of Veterans' Affairs told the ODT last month Trooper Frank Woodhouse, of the Otago Mounted Rifles, was his great-uncle.
He found the name on a memorial on the Gallipoli peninsula commemorating New Zealanders killed in the campaign.
''It was a profound experience and I do feel a little more connected now.
''There was even a photo of him. He looked not too dissimilar to me; he had some of the Woodhouse features.''
However it has emerged that the trooper shared only the Woodhouse surname with the MP.
Family spokesman Gareth Woodhouse told Fairfax media the trooper was his great-uncle and the family had his medals.
He had emailed the minister who replied with a "semi-apology".
"The family feels Michael Woodhouse should have done more research before making claims to the media about Frank Woodhouse."
Michael Woodhouse said he now accepted the man was not his great uncle and regretted any upsetting the family.
"I certainly didn't intend to offend them," he said.