Despite the lack of obvious progress yesterday, optimism was rising ahead of today's summit, with the markets beginning to price in the likelihood of a breakthrough deal today.
The euro rose against the dollar and the yield on Irish government bonds fell sharply.
Ten-year Irish government bonds are back at levels last seen on July 8, after the yield on 10-year bonds fell by more than .5pc yesterday to 12.8pc. The yield on two-year bonds dropped under 20pc for the first time in a week.
More important for the markets, yields charged to both Italy and Spain's 10-year bonds dropped to around the 5pc level yesterday, after yields passed 6pc for both on Monday.
Taoiseach Enda Kenny warned that the markets are watching the response of EU leaders but said the crisis in the euro area would not be resolved overnight.
Mr Kenny said there was "no one magic solution or silver bullet". But he said his priority at the summit of euro area leaders would be to ensure a deal with positive benefits for Ireland.
"I will be watching carefully and working to ensure that what is agreed for Greece doesn't in any way make our progress and eventual return to the markets more difficult," he said.
And he said he hoped the meeting would restore faith and "bring about certainty in the investment markets".
Influential economist Willem Buiter of Citi last night said Europe should simply scrap the margin it takes on Ireland's bailout loans. Mr Buiter said Ireland was being charged approximately a 3pc surcharge, leaving the overall interest rate at about 5.8pc.
"This would reduce interest payments per annum (when all loans of the current rescue programmes are disbursed) by €1.2bn in Ireland,'' said Mr Buiter.
However, he said long term he still believed Ireland would have to accept a default or restructuring of its debt.
"We continue to expect there will eventually be sizeable debt restructuring (with big haircuts) for Greece, Ireland and Portugal, perhaps phased over several years," said Mr Buiter in a new note.
He said he expected bond yields to continue widening throughout the summer regardless of developments at today's summit.
Christine Lagarde will attend the European Council meeting in Brussels, her first as head of the IMF.
European officials will now consider options previously rejected by Germany, including changes that would allow the European rescue funds to support markets by buying government bonds.
Other options up for discussion at the summit include enabling the main €440bn rescue fund to lend to recapitalise banks, giving countries a longer time to pay back loans and cuts to the bailout interest rates.
Together with a second Greek aid package, the goal is to prove to markets that Europe has the will and the tools to prevent the 21-month sovereign debt crisis from engulfing Spain and Italy.