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The West Coast mine has been closed since a methane explosion on November 19 in 2010, which killed 29 men. Two workers survived.
According to a spokesman for the Pike River families, Allied Concrete would no longer participate in the sealing of the mine and owner Solid Energy had been made aware of this.
Allied has contacted Sonya Rockhouse, whose son Ben was killed, to assure her they would halt supply until the dispute over re-entering the mine was resolved.
"We are incredibly relieved by this decision," Ms Rockhouse said today.
"Allied has shown real moral strength in stopping this work and is a great example of a good family business.
"We understand this means the sealing of the mine cannot go ahead, and we're grateful to Allied and to all of the Kiwis who have supported us to stop the mine being sealed.
"We have never lost faith in New Zealanders' belief in doing the right thing, and we're hoping that this sends a message to the Government to follow suit and to honour John Key's promise to get our boys out.
"We have international and local experts who say the drift is safe to enter. There may be the bodies of our boys in there as well as evidence that shines a light on what happened that terrible day.
"All we want is the chance to go in and check before our boys and any evidence is sealed away forever."
The Pike River mine incident ranks as New Zealand's worst mining disaster since 1914, when 43 men died at Ralph's Mine in Huntly.