Graham Melmoth, who became chief executive in November, described Mr Regan as "an irrelevance" who "does not stand a hope" of buying parts of the CWS's non-food businesses.
"It is a South Sea Bubble puff ... and I am not going to see the Co-op movement collapse into a share ramp," Mr Melmoth said.
He stressed that the CWS currently had no businesses up for sale and if some were to be sold for strategic reasons in the future then they would be sold "to maximise value, not to an asset-stripping middle man".
He admitted that the CWS would have to improve its performance and that the disparate parts of the movement would have to move closer together.
But he said the society had the backing of the 30-strong board and its 300 members. However, he said he could not rule out the possibility that Mr Regan might have some support from the membership.
Walter Douglas, secretary of Airth Co-operative, which has one village shop between Falkirk and Stirling, voiced his support for the Co-op yesterday. "We would fully support the CWS and vote against Andrew Regan," he said. "The CWS has been very supportive of us over the past nine or 10 years."
The view from the Deeside Farmers Co-op was rather different. "I don't know anything about it," a spokesman said. "We're just a farmers' buying group."
The Falklands Islands Co-operative could not be contacted.
Mr Melmoth's comments came as the CWS reported poor profits for last year.
Stripping out the contribution from the Co-op bank, which reported its results earlier this month, trading profits were 21 per cent lower at pounds 41.5m. The retained surplus was halved from pounds 31m in 1995 to just pounds 14m last year.
Mr Melmoth said a strategy review was under way which would see costs reduced and staff participation improved.
He also said that the Co-op "divi", which has been reintroduced in Northern Ireland and parts of Scotland, might be rolled out across the country.
Though he did not earmark businesses that might be sold, he admitted that the garages and opticians business would be reviewed. It also seems likely that some of the engineering businesses such as a safety footwear manufacturer will be regarded as non-core.
However, he dismissed suggestions that the food retailing operation, which is facing tough competition from the big supermarkets, would be sold: "There's no way we can get out of food retailing. It's a core part of the Co-op role."
The main reason for the decline in profits last year was a 14 per cent decline in profits at the food operation. This was largely due to difficult trading in Scotland where Tesco's purchase of William Low is thought to have increased competition.
Though some critics have said that the Co-op supermarkets may be losing money, the CWS said yesterday that its stores were trading profitably. However, it is clear that some superstores are struggling and it is possible some will be sold.
Profits at the specialist retail businesses, which include the funeral directors and travel agency business, are 12 per cent up at pounds 12.8m. Group sales were flat at pounds 3bn.
Mr Melmoth said his priority was mainstream retailing and he would target the CWS's 700 food and non-food stores to improve their performance.
Lanica Trust yesterday restricted itself to a brief comment on the CWS figures. "Overall it makes a diabolical return on a huge amount of turnover."