Mr Thoresen yesterday warned that customers would have to pay for advice and it is unlikely to be delivered in person.
The advice pledge was made by the Government as George Osborne loosened rules to effectively allow people to cash in their pensions and avoid buying an annuity.
Mr Thoresen, the former chief executive of Edinburgh-based pensions company Aegon, said: "It will be free to the customer in the sense they will not have to write a cheque. It will be paid for by the industry."
But he added: "It will have to be paid for and it will be paid for by the customer in the end."
Mr Thoresen told a hearing of the Treasury Committee that he could not provide an estimate of the likely cost of advice because there are still uncertainties about what is required.
Estimates have suggested that currently savers fork out around £630 each for the largely automated service of buying an annuity. Around 400,000 pension savers reach retirement every year.
In an announcement Mr Thoresen conceded was a "genuine surprise," the Chancellor said that cash withdrawals from pensions at retirement will be taxed at an individual's marginal rate, rather than the previous penal tax rates that encouraged the purchase of annuities giving lifetime income. Mr Thoresen said: "We do not think it would be sensible for this service to be face-to-face for everyone.
"For some people this service could be delivered perfectly well over the phone."
Pat McFadden, the Scot who sits as Labour MP for Wolverhampton South West, said: "It is not free, it is not advice, it is guidance and it might not be face-to-face."
Mr Thoresen said he expected those with pension pots of less than £30,000, some 60% of those reaching retirement, to take the savings in cash.
But he said advice would be more complicated for those with larger sums and would have to take into account factors such as caring responsibilities and the ability to continue working.
Mr Thoresen said insurers would seek to retain their relationships with existing customers but would have to prove any advice was impartial.
"I am very alive to this being something that has to pass the test of public opinion. I do think the industry could deliver this and deliver it cost effectively. But the test would be demonstrable impartiality," he said.
He said advice could be delivered via bodies such as the Money Advice Service or The Pensions Advisory Service.
Mr Thoresen denied that annuities would disappear but instead might be bought later in retirement.
The ABI complained to Mr Osborne last week about the leak of details of a separate regulatory inquiry into legacy insurance products. Yesterday, the Financial Conduct Authority announced that Simon Davis of law firm Clifford Chance will conduct an independent inquiry into its handling of the announcement.