Pike River families say they accept it is too difficult and expensive to continue with the drift recovery project.
The Pike River Family Reference Group, which represents families of 27 men who died in the Pike River mine, said the families accepted advice that going further would be expensive and complex.
In a statement, they said: "Families accept advice that going further would be a major, expensive engineering project, with complex potential safety risks, and it would be difficult to convince WorkSafe to give further exemption to mining licence."
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They said they accepted, "with heartbreak", Minister Andrew Little's advice that there would be no more government money to expand the project at this time.
The families hoped that the ongoing police investigation would continue to uncover evidence and said they would push if there was a potential for truth and justice.
"Families welcome advice that police with support of the agency, will drill additional boreholes to further their investigation of events underground that help them understand the disaster.
"In order to honour our men and leave a legacy the families want the deaths of our men to continue to make New Zealanders safer. We will work with the Public Service Commission and other agencies to further this goal."