BUPA has said the Taoiseach's comments about the company's withdrawal from the Irish market are misdirected.
BUPA's Chief Executive Martin O'Rourke said his company did not pick who could get cover.
He said the market allows people to choose their insurer, not the other way round.
Earlier, the Taoiseach had described as regrettable BUPA's decision to pull out of the Irish market.
Speaking after the EU Summit in Brussels, Bertie Ahern said community rating makes health insurance affordable to many in Ireland and BUPA knew the situation that existed when they moved into the country.
He rejected BUPA's contention that VHI is the only operator who can make a profit in Ireland.
Mr Ahern added we must now encourage and stimulate competition in the sector.
He said there is more than competition at play and it helps older people get insurance.
He said he is not going to listen to market forces comments from anybody.
The Minister for Health, Mary Harney, said the Government could not contemplate a situation where there is a monopoly in the health insurance market as it would be bad for consumers and bad for healthcare.
The minister is awaiting a report from the Competition Authority about how to make the health insurance market more competitive, before any break up of the VHI is considered.
Ms Harney was in Limerick today officially opening a new 10-bed unit at the Milford hospice care centre, which provides specialist cancer care services.
Speaking about the fallout from the BUPA decision, she said the Government is determined that the market will not be dominated by a monopoly.
That, she said, would not be good for consumers, for healthcare, or for public health policy.
But she insisted that competition must be based on risk equalisation.
Amicus would resist VHI break-up
Meanwhile, the Amicus trade union said it would resist any attempts to break up the VHI, where 800 people are employed.
Regional officer Colm Quinlan said the VHI had coped well with competition and that BUPA was pulling out of Ireland because it had been making huge profits which could not be sustained under risk equalisation.
The risk equalisation scheme requires companies with a lower risk profile to compensate others with older, more expensive members.
It is understood that the report from the Competition Authority will say that, for real competition to work, there needs to be at least four main players in the health insurance market.
Following Bupa's decision there will be just two.
Yesterday, Bupa Ireland said it was pulling out with immediate effect, and would end its cover for 475,000 members as their policies lapse.
The Competition Authority report will recommend that the VHI, which has over 1.5 million members, be broken up into a number of separate competing companies, and may necessitate the VHI brand name being dissolved so as not to give any new firms an advantage.
Earlier this month, the High Court ruled that the risk equalisation scheme was legal, which means that irrespective of its decision yesterday to pull out of the market, Bupa Ireland has still to pay the State an estimated €8 to €10 million under the risk equalisation scheme from January of this year.
The Government has promised legislation to put the VHI on an independent, commercial footing which in time will require it to meet minimum solvency levels and to compete on the same footing as other insurers.
