The victory of a pro-bailout party in Athens gives EU leaders space to act against the eurozone crisis but they still face huge challenges over Greece and Spain, over growth and on EU integration.
Relief came for eurozone governments as the conservative New Democracy party finished first in Sunday's election, beating the leftist anti-bailout Syriza party and easing the dangers of a euro exit.
But the respite was short-lived when markets turned against Spanish and Italian debt, putting the eurozone once again on the edge of chaotic crisis.
"A further lapse into the unknown was avoided on Sunday as New Democracy topped the vote in Greece," said Erik Nielsen, managing director at UniCredit Research, stressing however that more work remains to be done.
Though worries about political turmoil in Greece can be put aside for a day, the European Union's problems are far from over.
New Democracy must form a workable coalition with rival Socialists, a plan to rescue Spanish banks has yet to be finalised, a planned revamp of economic and monetary union is still on the drawing board, and deep divisions remain over how to spur growth ahead of an EU summit on June 28-29.
With the eurozone crisis in its third year, EU leaders are under immense international pressure to shift to a pro-growth strategy, deepen integration and avoid sparking a new global recession.
But Socialist French President Francois Hollande, in power for just a month although since elections on Sunday backed by a majority in parliament, is at odds with German Chancellor Angela Merkel over how to kickstart the eurozone economy.
Merkel has refused to back down from her austerity-first mindset, saying anything less amounts to mediocrity, while Holland has pushed for targeted spending of up to 120 billion euros of mainly re-directed EU funds.
The reaction on markets to the vote in Greece varied widely on Monday.
Asian stock exchanges finished up but European markets turned sharply from initial relief to renewed anxiety with borrowing costs for Spain rising to dangerous levels.
"There is still some room for disappointment to come in. This is a small bright spot and it could fade briefly," said Paul Mackel, head of Asian currency research at HSBC in Hong Kong.
With one in five Greeks without a job and recession deeply entrenched, Greek politicians want to renegotiate the stringent austerity measures imposed by the European Union and the IMF in return for massive bailouts.
German Foreign Minister Guido Westerwelle said on ARD public television that "there can't be substantial changes" in the commitments made by Greece but that he could "imagine we discuss again a delay" in achieving the targets.
"We risk entering a long and difficult period of negotiations with aid (loans) released in dribs and drabs over several months," a source close to the German government said on Friday at the prospect of a New Democracy win.
European leaders welcomed the Greek election result but avoided triumphalism as they faced G20 counterparts at a summit in Mexico focusing on the eurozone's years-old debt drama.
"We will continue to stand by Greece as a member of the EU family and of the euro area," EU president Herman Van Rompuy and European Commission chief Jose Manuel Barroso said in a joint statement.
"We look forward to working with the new government and to support the continued efforts of Greece to put its economy on a sustainable path," they said in the statement issued in Los Cabos, Mexico.
Agreement between Germany, Europe's top economy, and second-placed France is vital for any progress in EU discussions.
Meanwhile the eurozone's third and fourth-biggest economies, Italy and Spain, are in the crosshairs of investors who see them as the next weakest links following bailouts of Greece, Ireland and Portugal.
In a sign of lingering investor pressure, Spain's borrowing costs spiked above 7.0 percent -- a level considered unsustainable.
Federico Steinberg, economist at Spain's Elcano Royal Institute, cautioned against reading too much into the rising Spanish debt risk premium, saying a Spain bond issue due Thursday would be a better indicator of market sentiment.
"But the conditions for the 100-billion-euro Spanish banking rescue have still not been cleared up," Steinberg said. "The international markets are scrutinising this and we still know nothing of the conditions."
Eurozone finance ministers meet Thursday to discuss plans to provide Spain up to 100 billion euros ($126 billion) to save its banks, badly damaged from a property market collapse.