The euro has held steady as Irish Taoiseach Brian Cowen vowed to pass the 2011 budget before holding elections.
It follows a 1.5% fall against the dollar, after the Green Party, the junior partner in the government, said it wanted elections by mid-January.
Stock markets had also slid on the political uncertainty, led by a sharp fall in bank stocks.
"I'm saying that it is imperative for this country that the budget is passed," said Mr Cowen.
He conceded that early elections would need to take place, but only "after all the necessary arrangements have been put in place to give effect to a very important budget which it is imperative to pass".
Mr Cowen's comments followed calls from the opposition parties Fine Gael and the Labour Party to hold immediate elections.
The euro had rallied early in the day, following news over the weekend that the Irish Republic had agreed to a bail-out from the European Union and the International Monetary Fund (IMF).
But the single currency then gave up early gains as fears grew of early elections, dipping below $1.36 before recovering on Mr Cowen's comments.
Meanwhile banks were hard hit, with Lloyds, Royal Bank of Scotland and Santander all falling more than 4%.
Allied Irish Banks had fallen 3.9% by the close of trading, while Bank of Ireland was down 19%, more than giving up its gains from a meteoric rise on Friday in anticipation of the bail-out deal.
The negative sentiment continued into US trading hours, with the Dow Jones index falling 1.1% by early afternoon in New York, before recovering ahead of Mr Cowen's statement.
American financial stocks also fared particularly badly, with dealer-broker Goldman Sachs down more than 4%.
The Green Party's decision to push for early elections in January came as the government began the formal process of applying for up to 90bn euros (£77bn; $124bn) of European Union-led loans agreed on Sunday.
Meanwhile, two independent members of parliament upon whom the government depends for support said that they would not commit to vote in favour of the budget due before the end of this year.
The total level of the UK contribution is expected to to be about £7bn.
This includes contributions to European Union and International Monetary Fund (IMF) bail-out schemes, and direct bilateral loans.
The exact amount that Irish Republic will borrow will depend on the IMF's analysis of Dublin's needs over the coming days. The IMF is expected to provide about a third of the financing.
UK Chancellor George Osborne told BBC Radio 4's Today programme that it was in the UK's national interest to help the Irish Republic.
"Our two economies are connected, and our two banking systems are interconnected.
"Ireland is a friend in need, and we are here to help."
Defending the move later in parliament, Mr Osborne said "this is a loan and we can expect to be repaid".
He also ruled out the UK ever becoming part of a permanent bail-out mechanism for the eurozone proposed by other European governments.
The EU and IMF loans will be provided to the Republic over a three-year period.
Irish Finance Minister Brian Lenihan said the bail-out would also help to reduce the government's budget deficit to a target of 3% of GDP by 2014.
To help achieve this, the Irish government will publish a four-year budget plan on Wednesday, which is due to announce 15bn euro of austerity measures, including 6bn euros next year.
Dublin will also use the budget plan to outline how the country's banking industry will be restructured, with Irish banks expected to be turned into much smaller institutions.
Despite the bail-out announcement, and the Irish government's efforts to put in place austerity measures, credit rating agency Moody's has warned that it is "likely" to have to reduce its rating for the country.
However, Moody's added that despite the "multi-notch downgrade" it would still leave the Irish Republic with an investment-grade rating.