The Taoiseach has rejected Opposition calls for him to resign, saying the Government has a job to do to address the Budget and the four-year economic plan.
Labour Party leader Eamon Gilmore had called on Mr Cowen to step down, after what he called the 'blackest week' in Irish history since the Civil War.
Fine Gael leader Enda Kenny said Mr Cowen and his Government should resign in disgrace, while Sinn Féin's Caoimhghín Ó Caoláin said they should resign in shame.
Mr Cowen said that talks between the Government and officials from the International Monetary Fund, the European Commission and the European Central Bank on Ireland's debt crisis were going well.
The Government is seeking 'the best possible outcome for the Irish people' he added, and planned to chart its own way forward.
He said that while the country would keep many of the economic gains it had made, the talks could mean Ireland would have to take a step back in order to progress again.
Mr Kenny voiced his anger saying: 'The Government's appalling incompetence has resulted in the arrival of the IMF in this country and the potential sacrifice of our hard-fought economic sovereignty.
'The Government does not have the mandate or the authority to negotiate on behalf of the Irish people with the IMF and the EU.'
Green Party leader John Gormley has rejected calls for a General Election, saying the country is facing important decisions that cannot be taken during a campaign.
Mr Gormley said the arrival of the IMF could be a 'positive', as it offers the opportunity to restructure Ireland's economy in a way that should have been done years ago.
The Minister for the Environment told RTÉ News that if an election was called, there would be a caretaker Government that would have to conduct negotiations with the IMF, with no Opposition in place.
He said an election date could have been worked out when Opposition leaders met the Government to discuss a possible consensus, but it became clear that there was no prospect of cooperation.
Asked about Government denials of talks with the IMF, he said the distinction between discussions and negotiations 'was a Jesuitical one' that went over the heads of most people.
Mr Gormley acknowledged that there was a need for better communication by the Government.
However, he said that the Green Party was in Government to do its best to secure necessary changes.
Rabbitte accuses Govt of destroying economy
Last night, Labour Party TD Pat Rabbitte accused the Government of destroying the economy and of engaging in lies over the weekend.
Speaking on RTÉ's Prime Time, Mr Rabbitte directed his comments at the Government representative on the programme, Minister for Community, Equality & Gaeltacht Affairs Pat Carey.
However, Mr Carey accused Mr Rabbitte of engaging in polemic and of offering no solutions to the current difficulties.
He said the Government was determined to face up to its responsibilities.
Meanwhile, Minister for Health Mary Harney has said blame for the country's financial state lies with bank regulators, not with the Government.
She said the situation the country found itself in was completely unacceptable and very sad.
Speaking at a function in St Vincent's University Hospital in Dublin, Minister Harney also questioned whether the benchmarking process should have been introduced.
She said that in hindsight, public sector pay should have been compared with public sector pay in other countries, instead of private sector pay here.
The Government's four-year plan will be published early next week and was almost finished, following an eight-hour Cabinet meeting yesterday, she added.