But the Ministry of Primary of Industries has told the Herald there would not be another funding bid to the Cabinet.
Mr Twyford has slammed the decision.
"What it reveals is that the Government does not take seriously the crisis facing kauri, and I wonder what it will take to make them sit up and take notice.
"Does Tane Mahuta need to keel over and die before they realise this is a threat to more of New Zealand's most threatened species?"
While the ministry would remain involved in the programme after the finish of the five-year period in the middle of next year, it would assume a "national co-ordination" role, plants and environment response senior adviser Liz Clayton said.
The details of how the model would work will be developed during the next few months, and would look at how surveillance and monitoring, maintenance and hygiene, signage and tracking would be undertaken.
Auckland Council is seeking clarification on the Government's intended role in the future.
Sandra Coney, chairwoman of the council's parks, recreation and heritage forum, said it was not clear whether Government agencies intended to continue to work jointly with councils.
"We believe it is vital that we adopt a co-ordinated approach as the disease knows no boundaries," she said.
Waitakere Ranges Protection Society president John Edgar believed the Government needed to commit at least another $5 million.
Kauri dieback disease
What is it?
Kauri dieback is caused by the fungus-like disease Phytophthora taxon Agathis (PTA), formally identified in 2008. Microscopic spores in the soil infect kauri roots and damage the tissues that carry nutrients in the tree. Infected trees' symptoms include yellowing and loss of foliage, canopy thinning, dead branches and lesions that bleed resin at the base of the trunk.
Specific to New Zealand kauri, it can kill trees of all ages. Scientists are working to find control tools but there is no known treatment.
Where has it been found?
In the Waitakere Ranges Regional Park, on private land throughout the Auckland region, in the forest plantations of Omahuta, Glenbervie and Russell in Northland, Department of Conservation reserves at Okura, Albany, Pakiri, Great Barrier, Trounson Kauri Park and Waipoua Forest in Northland, home of our most iconic kauri, Tane Mahuta. It has not been found in many areas of Northland forest, the Hunua Ranges, Hauraki Gulf Islands (excluding Great Barrier) and the Coromandel Peninsula.
What's being done?
Councils in Auckland, Waikato, Bay of Plenty and Northland, with DoC and MAF Biosecurity, have been managing the threat with a five-year programme that ends next year. A new partnership model is being developed. Part of the programme is spreading public awareness. People are urged to clean their shoes and gear when leaving or entering forests with kauri growing.
