The Sports Direct tycoon had vowed to try to keep 80 per cent of the branches open after buying the department store chain out of administration for £90m last month.
So far 20 out of 59 in the UK have been saved, including the flagship Oxford Street outlet in London, following negotiations with landlords over new rental terms.
However Mr Ashley said he had been unable to agree terms with the landlords of the Edinburgh, Hull and Swindon stores.
Hundreds of staff across all the three branches are now going through redundancy consultation.
A fourth House of Fraser in Bath is also at risk of closure as the businessman continues to negotiate with its landlord, Bath City Council.
“I am disappointed that in my opinion a small number of greedy landlords still refuse to be reasonable,” said Mr Ashley, who also owns Newcastle United.
“Those landlords whom we have been unable to agree terms with include, but are not limited to, the following: Parabola Hope Street LLP, Redefine Paragon Square Hull Limited, and FI Real Estate Management Ltd.”
It is understood that landlords are reluctant to agree to the low rents the new owner is demanding.
The stores that will remain open are Altrincham, Aylesbury, Birkenhead, Camberley, Carlisle, Darlington, Doncaster, Grimsby, High Wycombe, Lincoln, London (Oxford Street), Middlesbrough, Plymouth, Skipton, Telford, Huddersfield, Leeds, Maidstone, Solihull and Sutton Coldfield.
Mr Ashley added: “We’ve showed what we can achieve on the British high street when we work together with landlords.
“I would like to thank those landlords who have helped us to rescue approximately 3,500 jobs at the stores we have saved to date.
“I am calling on everybody to pull together, including landlords and local authorities in order to help to save as many House of Fraser stores and jobs as possible on the great British high street.”
Birkenhead MP Frank Field said it was “tremendous” that the store in his constituency would stay open.
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“Six weeks ago, I wrote to Mike Ashley with an urgent plea to safeguard the future of our House of Fraser and the jobs of the store’s staff,” he said.
“Thanks to the positive discussions that have taken place since then with the store’s landlord, this cornerstone of our town centre is being given a chance to flourish once again.”
House of Fraser collapsed into administration after struggling to stay on top of costs, admitting that it could no longer afford to pay rents on a number of its stores.
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