LONDON – After more than three years of global market turmoil, political upheaval and nail-biting summits, European leaders are declaring the worst of the continent’s debt crisis behind them.

In New Year’s speeches and congratulatory comments, leaders across the region are crediting fresh rounds of painful austerity, a hard-fought new role for the European Central Bank and steps toward deeper integration with achieving a breakthrough.

Borrowing costs for troubled nations, they note, have come down steadily from last year’s dangerously high levels, pulling a string of countries back from the brink of imminent financial collapse and defying naysayers who predicted a quick breakup of the eurozone last year.

Yet any suggestion of victory in Europe may be viewed as the economic equivalent of President George W. Bush’s “Mission Accomplished” speech on Iraq aboard the USS Abraham Lincoln in 2003. Though market panic over Europe is subsiding, the region appears to be simply trading a crisis of financial markets for one rooted in its ailing economies.

Confronting the reality of deep budget cuts, higher taxes and piles of debt that have hindered any prospect of recovery, Italy, Spain and Greece are battling what economists predict will be yet another year of brutal recession.

Spain, in fact, may face a downturn even worse than the one seen in 2012, with its still-troubled regions and banks potentially prompting a bid for fresh bailout assistance. Even mighty Germany and France, the anchors of the 17-nation eurozone, potentially face weaker growth or stagnation this year.

Economists say those issues are set to once again make Europe the largest drag on the fragile global economy, dampening, for instance, demand for U.S. exports in the world’s single-largest trading bloc and home to 500 million consumers.

Europe is in a similar position as the United States, which avoided its own “fiscal cliff” this week but must confront the bigger questions of how to stimulate growth and bring down unemployment — which remained unchanged at 7.8 percent in December, according to data released Friday — while addressing the longer-term peril presented by high levels of national debt.

Analysts are also closely watching a string of triggers that could quickly reignite a market panic, including Greece’s implementation of bigger reforms this year and the deepening social crisis in Spain.

Indeed, rather than getting to the roots of Europe’s debt problems, the region’s politicians have largely put off a day of reckoning, economists say. Some argue, for example, that the biggest basket case in Europe — near-bankrupt Greece — could be forced out of the currency union by mid-2014, if not earlier.

“A couple of things have happened that have taken away the immediate big breakup risk of the euro,” said Juergen Michels, senior economist at Citibank in London. “But the underlying problems and the huge debt in Europe are not yet solved. This crisis is not over. We see further problems ahead.”

The financial woes that started in Greece in October 2009 engulfed one heavily indebted European country after another, roiling global markets, degenerating social conditions in hard-hit nations and prompting a voter backlash that saw leaders swept out of office in Ireland, Spain, France and Greece.

To be sure, there are signs of fiscal improvement. Excluding the massive interest payments on their debts, both Italy and Greece are posting budget surpluses after gutting spending and raising taxes, and Spain saw a surprise improvement in December unemployment, though the jobless rate remains around 25 percent.