Opposition Fine Gael took nearly 32% of the vote in local polls, according to latest results, beating Cowen's Fianna Fail party into second place with 23%, and tabled a motion of no confidence in the government next week. However, Prime Minister Brian Cowen vowed to stay in office until the end of his government's term in 2012.
More than half a million people are estimated to have voted, giving a turnout of just over 60%, on a par with the country's European election turnout in 2004.
Cowen, who took over as prime minister a year ago, is expected to survive the vote in parliament but could face a revolt within his party later in the year, analysts said.
A coalition between right of centre Fine Gael and the left-wing Labour party would be the most likely outcome of a general election, the poll showed.
"The tide of public opinion is against us at the moment," Cowen said. "But we have to continue with the work we have set out, that is to fix this recession [...] and to use the mandate we have until 2012 to do so."
Fianna Fáil has dominated Irish politics since the 1930s but is facing unprecedented voter anger for failing to prevent the former 'Celtic Tiger' economy falling into severe recession and raising taxes to try to end twin fiscal and banking crises.
George Lee, a former economics broadcaster and longtime critic of government policy, sailed to victory in a parliamentary by-election that will cut Cowen's majority to around 51%, making it increasingly difficult for him to push through unpopular fiscal measures.
Fianna Fáil received a drubbing in a second parliamentary by-election in Dublin in which Maurice Ahern, brother of former prime minister Bertie, was battered into fifth position and left fighting for his council seat.
Opinion polls, including Sunday's RTE/Sunday Independent survey, show a clear majority of voters support the EU's Lisbon Treaty as they look to Europe as an economic safety net in uncertain times.
But the possible loss of one of Fianna Fáil's four MEP seats to Eurosceptics signals that the Lisbon Treaty's endorsement will not be automatic in a likely October referendum.
Economy the key
The government's drubbing has rattled the junior coalition partner, the Greens, whose support is crucial for Cowen.
"That will open up the question of should we be in government or should we not be in government," Ciaran Cuffe, one of six Green MPs, said of his party's poor performance.
But it would be politically dangerous for the Greens to pull the plug now, and Cuffe signalled the party would instead demand more influence on policies to keep a lid on grassroots disquiet.
"I think it could be the start of a new phase of government, where you will see a greener tinge in the environmental sense of the word," he said.
Analysts said Cowen's position could be at risk after an expected second referendum on the EU's reforming Lisbon Treaty in October if the economy is not showing signs of life.
"After the referendum, if things have not picked up [...] people will be making calculations to see if their seats are safe, which they won't be of course, and will be looking for change," said Neil Collins, a professor at University College Cork.
Early tallies suggested Fianna Fáil could lose one European Parliament seat, which was likely to go to opponents of the Lisbon Treaty.
The official results of the European elections will not be released until after 22.00 CET on Sunday, when polling stations in all EU member states have closed.
(EurActiv with Reuters.)
