Minister for Health Mary Harney is expected to come under pressure in the coming days to declare her future after Progressive Democrats' members voted yesterday to disband the party.
There is speculation that Ms Harney, a former PD leader, will stand as an independent with the party likely to be wound up early next year after members voted in Mullingar, Co Westmeath, to end the party.
The demise of the PD organisation raises questions about Ms Harney's political mandate as a senior Government minister and casts some doubt on the coalition.
Ms Harney has ruled out running for the next Dáil, but she told RTE radio this afternoon that she would like to continue in her Cabinet position.
"I love being Minister for Health. It's a difficult and challenging job but I think we're making progress," she said.
However she said it was a matter for the Taoiseach to decide whether she remained in the position.
"I love the job but I've no right to be there, I've no entitlement as a person to be there. It is purely a matter for the Taoiseach to decide whether or not I continue as Minister for Health."
She also said it would be "very wrong" to blame Michael McDowell for the demise of the party.
"It would be very wrong to lay the blame at Michael McDowell's door. We all have to take responsibility. We've had huge successes and maybe we've made mistakes but at the end of the day the people of Ireland did not give us sufficient support to be able to elect people to the Dail and continue as a viable policital party, " she said.
More than 400 delegates heard arguments for and against staying in politics at a specially convened conference, but a passionate speech made by Ms Harney is believed to have convinced undecided members to vote 201-160 vote in favour of a winding down.
A letter from party founder Des O'Malley that was read out to delegates called for the Progressive Democrats to be disbanded, and party leader Senator Ciarán Cannon supported this view.
The party, which was formed out of bitter divisions with Fianna Fáil 23 years ago, had been teetering on the verge of collapse since suffering heavy losses at last year’s general election.
Commenting on the decision by the PDs to wind up as a political party,Fine Gael Leader Enda Kenny said this evening there had been a 'genuine sense of excitement in political circles at the time of the foundation of the PDs, an excitement that proved difficult ultimately to sustain.
However he called on the Taoiseach to clarify the position of Mary Harney as the Minister for Health.
"Looking to the future, it is now the case that Mary Harney will be an Independent TD sitting in Cabinet. Fine Gael has made clear in the past its opposition to the health policies adopted by this Minister and Government," he said.
"It is now important that Brian Cowen clarifies the position of status of the soon to be Independent TD Mary Harney as his Health Minister into the future."
Additional reporting PA