The continent faces its "harshest test in decades," and this year "will no doubt be more difficult than 2011," German Chancellor Angela Merkel said.
"The path to overcoming this won't be without setbacks, but at the end of this path Europe will emerge stronger from the crisis than before," she told a national television audience Saturday.
A year ago, she praised Germans for "mastering the crisis as no other nation."
Germany is Europe's largest exporter and largest economy.
French President Nicolas Sarkozy, who faces a re-election battle in the spring and is trailing in polls, echoed Merkel's somber remarks.
"This extraordinary crisis, without doubt the gravest since the Second World War, is not over," he said.
"In the storm, you have suffered. I know that the lives of many of you, already tested by two difficult years, are being severely tested once more," with greater worries now than a year ago.
But there is "reason for hope," and "a new Europe" can emerge from the crisis if France and Europe face their challenges and act on them, he said. Otherwise, "if we stand still," there is reason for danger, he said.
In a week Merkel and Sarkozy are to discuss a new fiscal treaty, agreed by all 27 European Union members except Britain last month, to impose stringent budget requirements on EU nations. Then three weeks later EU leaders are to gather in Brussels to discuss ways of spurring growth.
A final accord on the summit treaty is due in March.
"Sacrifices are necessary to ensure the future of young people -- it's our objective and a commitment we cannot avoid," Italian President Giorgio Napolitano said on national television Sunday.
"Nobody today -- no social group -- can avoid the commitment to contribute to the clean-up of public finances in order to prevent the financial collapse of Italy," he said.
"The sacrifices won't be useless," he said. "Only united can we progress and count as Europeans in a radically changed world."
Italy also has no future without regenerating the political system, Napolitano said.
The euro crisis forced borrowing costs higher for Italy and Spain and led to the dismissal of Silvio Berlusconi's center-right government in Rome and the fall of the Socialist administration of Jose Luis Rodriguez Zapatero in Madrid.
Spain's new government said Friday its 2011 budget deficit would reach 8 percent of gross domestic product, rather than the 6 percent target set by the previous administration.
In Greece -- the first European country to seek a bailout, in 2010 -- Prime Minister Lucas Papademos, appointed to lead an interim government in November after the resignation of George Papandreou, said there would be no let-up in the austerity measures, which many Greeks feel are too tough. He asked for resolve in a difficult year.
"We have to continue our efforts with determination so that the sacrifices we have made up to now won't be in vain," he said in a televised address.
Notable deaths of 2014 [PHOTOS]