But he raised hopes that trees could be identified which were resistant to Chalara ash dieback, and said the disease did not necessarily spell the end of the British ash.
Following another meeting of the Government's emergency committee on tackling Chalara ash dieback, it was revealed that there were now 129 confirmed sites where the disease had been found, including 64 cases in woodland.
The Chalara fraxinea fungus, which causes leaf loss and crown dieback and can lead to tree death in ash trees, has wiped out 90% of ash trees in some parts of Denmark and is becoming widespread throughout central Europe. There are fears that the UK's ash trees are facing a similar fate to its elms, which were destroyed by Dutch elm disease in the 1970s.
In an action plan, the Government ruled out cutting down and burning mature ash trees to stop the disease. Mature trees are valuable to wildlife, take longer to die and can help experts to learn more about genetic strains that could be resistant to the disease, officials said.
The action plan will focus on tracing and destroying newly planted trees and those in nurseries, and better understanding the disease through research and surveying. The search for the disease will include ash trees in towns and cities as well as the countryside, while there are plans to raise awareness among industry, conservation groups and the public on how to identify diseased trees and those likely to be resistant.
Mr Paterson said: "The scientific advice is that it won't be possible to eradicate this disease now that we have discovered it in mature trees in Great Britain. However, that does not necessarily mean the end of the British ash. If we can find those trees with genetic resistance to the disease and to restructure our woodlands to make them more resilient."
Earlier this week industry, conservation groups and scientists met for a summit on how to deal with ash dieback. Mr Paterson said: "The very clear advice from the summit was don't chop down the mature trees, even if they've got it, because amongst them is the odd specimen that will be resistant."
Ministers have already brought in a ban on importing ash trees from outside the UK, and movement restrictions from infected areas in this country, in a bid to stop ash dieback spreading further from imported trees. But experts have warned that the disease in mature woodlands is likely to have been wind-borne from the continent and little can be done to stop its spread.
The National Trust welcomed the decision not to chop down mature trees, and backed the commitment to destroy young plants, but said it was surprised the Government believed it will not be possible to eradicate the disease. Dr Simon Pryor, director of natural environment at the trust, said: "Given our limited understanding of this disease in this country, we believe we should keep an open mind as to whether it may be possible to eradicate it, or at least contain it within the core area in the east."