ATHENS (AP) ― Greece’s lawmakers overwhelmingly approved next year’s austerity budget early Wednesday, extending tough spending cuts that have already left Greeks struggling as the country tries to slash its vast debts and tame a severe recession.

With three parties, including the majority socialists and their rival conservatives, participating in Greece’s new coalition government, the budget was passed with a 258-41 majority in the 300-seat Parliament.

“This is a difficult budget ... with ambitious targets,” Prime Minister Lucas Papademos told lawmakers just before the after-midnight vote. “But we must achieve our targets and implement the measures that are foreseen.”

“The financial crisis in our country is not a passing storm,” Papademos warned. “Given the size of the problems, our national effort will not be completed in 2012. It will take many years, and will require the efforts and insistence of several governments.”

Greece’s acute debt woes have triggered a Europe-wide crisis and the country is surviving on international rescue loans, released on condition it implements deeply resented cutbacks. The crisis has even prompted talk of the country being forced out of the eurozone ― or even the European Union ― both of which Papademos insisted were out of the question.

“Our position in Europe is not negotiable,’’ he said. “The Greek people will defend it by all means. But participation in the euro involves rules and obligations, which we must consistently meet ... Greece belongs to Europe, and Europe cannot be envisaged without Greece.’’

The end of the budget debate coincided with the third anniversary of a fatal police shooting of a teenager in central Athens, and as lawmakers spoke clashes broke out in front of Parliament between hundreds of anarchists and riot police during a commemorative march.

Masked youths hurled stones, bottles and firebombs at police, who responded with volleys of tear gas and stun grenades on Tuesday night. Earlier in the day, violence also broke out on the fringes of a separate march by about 2,000 students outside Parliament.

Speaking inside the building during the debate, conservative party leader Antonis Samaras said his objections to many of the austerity measures already passed remained, but that he was backing the budget as the priority now was to reduce the debt.

“We are voting today for the budget, firstly because we are giving immediate priority to ensuring the viability of Greek debt and to maintain the targets of fiscal adjustment,’’ he said.

Samaras was a vocal critic of the austerity measures over the past two years, insisting that increased taxation in particular was the wrong method and that taxes should be cut in order to stimulate the economy.

The conservative leader said the crisis had also shown up problems within the eurozone.

“It has been proved that repeated efforts until now to stabilize the euro have failed,’’ he said. “And that the euro crisis is not only due to Greece’s bad fiscal situation, but also to the eurozone’s inability to deal with its problems.’’

The 2012 budget foresees a fourth year of recession with the economy contracting by 2.8 percent, a target which Finance Minister Evangelos Venizelos said is “ambitious but achievable.’’

It also projects a primary surplus ― a surplus excluding interest payments on debt ― of 1.1 percent of gross domestic product.

Greece’s debt troubles have roiled the euro, with Europe’s single currency facing its largest crisis since it went into circulation in 2002. The Standard & Poor’s ratings agency placed 15 of the 17 eurozone countries on notice for possible downgrades. The only two it left out were Cyprus, whose bonds have near-junk status, and Greece, whose low ratings suggest it is likely to default on its debts soon anyway.

On Monday, German Chancellor Angela Merkel and French President Nicolas Sarkozy urged changes to the EU treaty that would centralize decision-making on spending and borrowing for the eurozone. Tighter political and economic coordination among euro countries is seen as a precursor to further financial aid from the European Central Bank, the International Monetary Fund, or some combination.

Greece has been relying for financial survival on billions of euros (dollars) in rescue loans from other eurozone countries and the International Monetary Fund since May 2010. In return for the first bailout, the country imposed a series of harsh austerity measures, including salary and pension cuts and repeated rounds of tax hikes that have left the country mired in a deep recession.

Despite the measures, the government found itself persistently missing the fiscal targets set out in its first bailout. A second rescue package worth 130 billion euro ($175 billion) was put together in October, and includes plans for private creditors to write off 50 percent of their Greek bonds, potentially cutting the country’s debt by 100 billion euro. Negotiations on the details of the deal are expected to extend into the new year.

A sudden announcement last month by then prime minister George Papandreou that he would put the hard-fought deal to a referendum triggered a political crisis that forced him to step down and a coalition government be formed. Former central banker Papademos has been appointed to lead the interim government until early elections, tentatively set for February.

The crisis has taken its toll on the popularity of Greece’s main political parties, though Papandreou’s Socialists have taken the severest hit. Just two years after a landslide election victory with 44 percent of the vote, they are polled at enjoying just 15.3 percent support and trail the conservatives who have 21.5 percent, according to a GPO survey for Mega television.

The poll of 1,400 adults was conducted between Nov. 30 and Dec. 5. No margin of error was given.

According to the poll, the vast majority of Greeks ― 80.7 percent ― believe the country’s financial situation will deteriorate further in 2012, while 79.3 percent believe Greece’s rescue deal with the EU and IMF failed to resolve the debt crisis.