Prime Minister John Key is rejecting a call for the former Department of Labour Minister to go from the Cabinet altogether.
Kate Wilkinson quit her Labour portfolio following the release of a highly critical report on the Pike River Coal mine disaster on Monday, but retains other ministerial warrants including Food Safety, Associate Immigration and Conservation.
Twenty-nine men were killed at the West Coast mine following a series of explosions that began on 19 November 2010. Only two workers survived after managing to get out of the mine following the initial blast.
The Department of Labour came in for particularly heavy criticism for failing to properly supervise operations at the mine.
The Royal Commission said the department did not have the focus or capacity to ensure that the Pike River company was meeting its health and safety responsibilities and it should have stopped the mine from operating.
Kate Wilkinson said her resignation from the Labour portfolio was a personal decision and Mr Key says the minister felt it was the honourable thing to do.
But Labour Party's primary industries spokesperson, Damien O'Connor, asked Mr Key why she is keeping her Cabinet position on full pay, given the 29 deaths.
Mr Key said no resignation would give those men's families the support they need.
"But let's go back to the Royal Commission. The Royal Commission was quite clear the primary responsibility for health and safety rested with the company. They they utterly failed."