"I just indicated to him what I've said publicly, that I'll consider meeting with them," English said.
Despite his willingness to meet with the families, he said he did not want to mislead them by suggesting there was "a political decision that could make that mine safer than it is".
That was disputed by Labour leader Andrew Little, who said the Government was able to intervene because it owned the mine's operator, Solid Energy.
"The Government can make this decision. In the end, it is a political decision."
For this reason, he did not think a separate Government entity to manage the mine was needed.
Little said English should "do the compassionate thing" and work with the families on a re-entry plan. Solid Energy and the families appeared to have conflicting expert advice, he said, and only way forward was for the Government to commission an independent expert.
NEW PLAN
The families' new report was written by David Creedy, a vice chair of the UN Group of Experts on Coal Mine Methane and former UK Principal Mines Inspector Bob Stevenson. It was peer-reviewed by two mining experts.
It said technical advisors to the victims' families "remain convinced" the mine could be entered safely.
"The key factor is that no person will enter the drift until a fresh air atmosphere has been established and measures are in place to control major hazards," the authors said.
"The entry plan has been reviewed and agreed as credible by independent experts."
The authors said they accepted Solid Energy would not accept their proposal. Therefore, only direct Government intervention could decide the outcome.
"It would appear that re-entry would only proceed if [Solid Energy] no longer had any responsibility for the mine.
"A new ownership structure will therefore be required to allow the re-entry to proceed."
The report said changing conditions, including more stable gas concentrations, had simplified access to the mine. Re-entry to the drift would allow detailed examination of the mine and could help prevent further tragedies, the authors said.
"There is no technical mining reason that re-entry into Pike River Drift could not be achieved safely," the authors concluded.
"A detailed plan should be developed to deliver such a result."
Sonya Rockhouse, whose son Ben died in the disaster, said the new plan showed it was time for the Government to sit down with the families and negotiate a re-entry.
"This isn't just about getting out boys out, it's about getting into the drift to get evidence of what happened down there."