Enda Kenny is attending his first summit of EU heads of state as Taoiseach, with Libya and the Eurozone crisis set to dominate proceedings.
The European Council meeting will consider the situation in Libya and the surrounding areas, while the Eurozone gathering will focus on economic co-ordination and related issues in the euro area.
Mr Kenny will be pressing for an opportunity to discuss easing the terms of the IMF/EU bail-out during the meeting of the Eurozone heads of state.
Both Fine Gael and Labour made fighting for better repayment terms for last December's 85 billion euro rescue package a key plank of their election campaigns.
Mr Kenny met European Commission President Jose Manuel Barroso in Brussels earlier in the week ahead of Friday's summit.
The Commission described the meeting as frank and positive, with Mr Barroso acknowledging the interest rate on the IMF/EU rescue deal was a major issue during the election.
"President Barroso reiterated that the Commission supports Ireland's wish to have some easing of the interest rate which applies to the loans negotiated under the programme," a Commission statement said.
"The president expressed hope that room for manoeuvre in the European Council can be found which achieves the Commission's and Ireland's common aim of making it easier for Ireland to get back on its feet."
But Mr Kenny faced his first hurdle when German Chancellor Angela Merkel said she would back a lower interest rate if Ireland weighs in behind a common EU-wide corporate tax base - potentially threatening Ireland's controversially low 12.5% rate.
As he entered the summit Mr Kenny said: "I've come here, being two days in government, with a very strong mandate from the Irish people for an improvement in the terms of the IMF/EU deal. I intend to set out the reasons why they should apply."