Greek prime minister puts figure on new bailout needs for first time as he struggles to get country behind austerity measures

Greece will need a second international financial bailout of the same magnitude as last year's €110bn (£97bn), in order to avoid a tumultuous debt default, the prime minister, George Papandreou, has conceded while mounting a last-ditch appeal to parliament and the nation to back his austerity programme.

Appealing for a vote of confidence in his newly reshuffled government, the Socialist party leader warned that, without further aid from the EU and IMF, Athens's cash reserves would soon run out, inviting a financial crisis that European officials have warned would rapidly contaminate the international financial system.

"I ask for a vote of confidence because we are at a critical juncture," said Papandreou in a speech opening a marathon parliamentary debate which will culminate with the crucial vote on Tuesday.

The sacrifices required for that aid – more cost-cutting, tax increases and job losses, plus massive privatisations – were infinitely better than a default, he said, as thousands of austerity-weary Greeks protested outside the 300-seat parliament.

"The debt and deficits are national problems that have brought Greece into a state of [diminished sovereignty], one that may have protected us from bankruptcy, but which we need to get out of.The consequences of a violent bankruptcy, or exit from the euro, would be immediately catastrophic for households, the banks and the country's credibility … the sacrifices people are making are paying off," he said.

It was the first time that Papandreou or any Greek official had broached the subject of how big the new bailout would be.

The admission, after weeks of speculation over the size of the package, highlighted the state of the economy despite it receiving regular cash injections from the €110bn rescue agreed last May, the biggest bailout in western history.

Athens's debt, which stood at €340bn in December, was estimated to have exceeded €355bn, the equivalent of 150% of GDP, in April. By comparison, the government's annual income is almost one-tenth of that, at around €40bn.

Papandreou called the vote after a first attempt to pass more austerity measures in return for the aid met with fierce opposition from his own Pasok party. After a flurry of defections and the collapse of talks aimed at a coalition government with the opposition, he moved ahead with a radical reshuffle of his cabinet, appointing Evangelos Venizelos, a party heavyweight and political rival, as finance minister to navigate Greece through its worst crisis in modern times.

A poll published in the To Vima newspaper showed 47% of respondents vehemently opposed to the new €28bn cost-cutting plan, whose centrepiece is an ambitious privatisation drive that aims to raise an additional €50bn by 2015.

Before attending his first summit of eurozone finance ministers in Luxembourg where the details of a new three-year rescue deal for Greece were discussedon Sunday, Venizelos promised austerity measures would be meted out fairly. But unions are preparing a series of strikes.

Papandreou rejected a call from the conservative opposition leader, Antonis Samaras, to step down. Instead, in an attempt to win over voters, who identify politicians with corruption, Papandreou said he would call a referendum later this year on changes to the "political system": an overhaul of the constitution, and the abolishing of practices such as the immunity enjoyed by MPs, a source of the discontent that has led protestors to scream "thieves" outside parliament.

However writing in today's Daily Telegraph Boris Johnson, the London mayor, called for Greece to be allowed to go bankrupt, leave the euro and "forge a new economic identity with the new drachma".

"The euro has exacerbated the financial crisis by encouraging some countries to behave as recklessly as the banks themselves," Johnson said.

The conservative opposition leader, Antonis Samaras, called for Papandreou to step down to pave the way for elections and a renegotiation of the bailout. But Papandreou called for the opposition to "stop fighting in these critical times, stop sending the image that the country is being torn apart".