European leaders agreed to launch a fresh bailout of Greece subject to parliamentary passage of an austerity package next week. Britain is to be spared from taking part in the rescue after leaders accepted David Cameron's argument that the bailout, expected to total up to €120bn (£107bn) should be borne by the other 16 countries using the single currency.

The Brussels summit of the EU's heads of government was scheduled to focus on the European economy, immigration policy and upheavals in the Middle East, but was overshadowed by the sovereign debt crisis in Greece, which is perceived to be on the brink of a meltdown that might trigger a fresh international banking crisis.

A statement said that the draconian package of €28bn in spending cuts and tax rises plus a €50bn privatisation programme "must be finalised as a matter of urgency in the coming days" by Greece to qualify for the new bailout.

The rescue would be provided by Greece's "euro partners and the International Monetary Fund", meaning that Britain would be exempted from the European part of the package.

In Prague , Cameron reiterated his refusal to take part in the latest Greek bailout except through Britain's contributions to the IMF.

Germany had been insisting that the bailout should be partly funded by all 27 EU members, but backed off. "It would have been too divisive while not supplying very much money, so there was no point making an issue of it," said a European commission official.

"It's not part of the package," said Herman Van Rompuy, the European council president who chaired the summit, of the fund to which the entire EU contributes.

"This is the right outcome for the British taxpayer," said a Downing Street source.

Washington and the IMF have been piling the pressure on EU leaders to deal decisively with the Greek emergency.

While George Papandreou, the Greek prime minister, was fighting for his political life and with Greece's fate in the balance, the opposition leader, Antonis Samaris, also came under pressure from EU leaders to line up behind his political foes for the sake of the nation.

At a meeting of European centre right leaders in Brussels before the summit, Germany's chancellor, Angela Merkel, and others pressed Samaris to drop his opposition to Papandreou and to support the austerity package in parliament. Samaris has sworn his opposition and his New Democracy party all voted against Papandreou in a vote of confidence early on Wednesday morning.

The EU, the IMF, and the European commission all say that the Greek austerity package has to be carried by the broadest possible majority next week.

In July and August, the Greek government has to redeem bonds to the tune of €9.4bn. Without €12bn from the eurozone and the IMF – the fifth tranche of last year's 110 billion bailout – by mid-July, Greece will be broke, sparking a sovereign default and a bigger international crisis.

The Greek finance minister, Evangelos Venizelos, announced details of the austerity measures, which include lowering the minimum threshold for income tax to €8,000 a year from its current level of €12,000.

Greece will also levy a one-off solidarity tax ranging from 1-5% depending on income, increase tax on heating fuel, and impose a minimum tax on the self-employed, who are widely regarded as some of the country's most flagrant tax evaders.

To try to ease Greece's plight, José Manuel Barroso, the European commission president, pleaded with EU governments to agree to fast-track €1bn from the EU budget to Greece for poverty and unemployment relief.