The UK's biggest mutual believes Euan Sutherland's proposed remuneration package is in line with comparable firms and reflects the scale of the task ahead.
But the pay award comes at a time when the group is facing largescale job cuts after a disastrous year in which its banking arm needed rescuing due to a £1.5bn shortfall.
It is understood Mr Sutherland, 45, will receive a base salary of £1.5m this year, plus a £1.5m retention payment. With pension contributions and compensation for buying out his previous contract, he will receive £3.66m this year.
The group, owned by its eight million members, is reportedly set to announce losses of £2bn later this month, having seen its banking arm come under the control of bondholders.
Stewart Hosie, the SNP's Treasury spokesman, said: "People will be totally baffled that, once again, failure - and in this case near collapse - is being rewarded by what looks like a huge pay and bonus bonanza. It looks like the Co-op just doesn't get it".
Shadow Chief Secretary to the Treasury Chris Leslie said the salary proposal was "very disappointing".
He added: "The Co-op should be acting differently. They have some big challenges and I hope they can overcome those and I support them in doing that. But they recently put out a questionnaire to the public about their objectives and I didn't see in that questionnaire anything about 'Do you agree with extending high remuneration for senior executives?'".
Lord Oakeshott, former LibDem Treasury spokesman and a Co-operative customer, said: "Gigantic golden hellos for the new bosses send the wrong message to millions of loyal members, customers and staff. Of course managers should be well rewarded - when they've turned the business around sustainably."
Glasgow-born Mr Sutherland joined the Co-op in May last year from Kingfisher, where he was chief operating officer.
He was educated at the High School of Glasgow and read accountancy at Edinburgh University before doing Business Studies at Aston University in Birmingham. After training in marketing with Coca Cola, he worked in marketing management positions with Mars, Matalan, Currys and Superdrug.
Since May Mr Sutherland has been trying to revive the Co-op's standing amid revelations of drug use by the Co-op Bank's then chairman, Paul Flowers, and the near-collapse of its banking arm.
Ursula Lidbetter, chairwoman of the Co-operative Group, said: "We saved the bank, without recourse to the taxpayer and we are now embarking on the long and complex journey to revitalise the wider group.
"It is against that backdrop that we recruited Euan Sutherland and a top team with the skills and experience needed at this crucial stage in our history, reflecting the necessity for change.
"The remuneration packages of our executives are in the middle of a range of comparable companies. This represents an increase on the pay of their predecessors to reflect the greater commercial, management and turnaround experience they are bringing to bear.
The revelations over Mr Sutherland's salary reawakened the debate over executive pay in the banking sector and follows on from anger last week when it emerged almost 500 Barclays and 75 Lloyds Banking Group staff were being paid more than £1m each a year, sparking claims a bonus bonanza had returned to the City.