ATHENS (AFP) - Prime Minister Alexis Tsipras on Tuesday promised Greeks he would not abandon ship despite fractures within the government over draconian reforms that eurozone creditors have demanded in exchange for a bailout.

On the eve of a crucial parliamentary vote on the widely unpopular measures, Mr Tsipras said he took "full responsibility" for signing an accord he did "not believe in, but which I signed to avoid disaster for the country", in the face of a real risk Greece would crash out of the common currency.

The International Monetary Fund warned late Tuesday however that Greece's EU creditors will still have to go "far beyond" their existing estimates for debt relief to stabilise the country's finances, pointing to the "considerable" downside risks.

In the last-ditch agreement struck Monday, the parliament in Athens must pass sweeping changes to labour laws, pensions, VAT and other taxes.

Only then will the 18 other eurozone leaders start negotiations over what Greece is to get in return: a three-year bailout worth up to 86 billion euros (S$129 billion), its third rescue programme in five years.

But threats from some 30 rebel lawmakers in Tsipras's own radical left Syriza party have forced the prime minister to turn to pro-European opposition parties to push the deal through, and raised questions in some quarters about his political survival.

"A prime minister must fight, speak the truth, take decisions and not run away," he said in an interview on Greek public television, when asked whether he would resign if the reforms fail to pass or he loses his parliamentary majority.

He said he was "a captain on a ship in difficulty, and the worst thing to do would be to abandon ship".

Fresh polls published late Tuesday by Kapa Research found 72 per cent of Greeks surveyed thought the deal was necessary, with the majority blaming Europe for the "tough measures" rather than Mr Tsipras's government.

But a number of prominent Syriza leftists, whose party took power in January on an anti-austerity ticket, were highly sceptical of the deal.

"The great majority of Syriza organisations oppose this agreement... in terms of labour and pension issues this is worse than the last two bailouts," lawmaker and parliament vice-president Despoina Haralambidou told Vima FM radio.

Syriza's junior coalition partner, the nationalist Independent Greeks party (ANEL), said it would not approve the measures but would stay in the government.

Despite strong opposition, Mr Tsipras yielded to a plan to park assets for privatisation worth up to 50 billion euros in a special fund, with some 25 billion euros of the money earmarked to recapitalise Greece's banks.

The PM said the establishment of the fund meant ordinary Greeks' savings were safe, but added that the reopening of the banks - which have been closed for over a week - depended on the finalising of the deal, which could take a month.

The European Central Bank has been keeping Greek banks afloat with emergency liquidity, but so far has refused to provide extra funds needed to reopen lenders.

Mr Tsipras has predicted "the great majority of Greek people" will support the deal, which he said includes help to ease Greece's huge debt burden and to revive its crippled banking system.

But when asked whether the risk of a Greek exit from the eurozone - a so-called "Grexit" - had been averted, he said he "cannot say with certainty until we have signed" the final bailout agreement.

French President Francois Hollande insisted there was no humiliation for Greece in the deal struck in Brussels, while US President Barack Obama hailed the deal as a "positive step" but said that "further work will be required".

Many ordinary Greeks are sceptical the deal can bring any improvement to their lives. Some expressed their anger on social media, with the Twitter hashtag #ThisIsACoup trending.

Greece's public servants are also to stage a 24-hour strike on Wednesday, the first big stoppage since Tsipras took power.

Faced with a euro zone deeply distrustful of Athens after five months of tense meetings, 40-year-old Tsipras had to agree to demands that critics say rob Greece of financial independence.

But while he admitted "there have been mistakes", he defended his government's six-month battle with its creditors and refused to blame his flamboyant former finance minister Yanis Varoufakis for complicating matters, saying "a perfect economist does not mean one is also a politician".

If Greece does pass the agreement, Europe's next step would be to push the deal through several national parliaments, many in countries that are loath to afford Athens more help.

Germany's Bundestag is likely to vote on Friday, provided the Greek parliament rushes through the four new market-oriented laws by Wednesday.

A new poll said 55 per cent of Germans supported their chancellor, Angela Merkel, on the bailout deal, while a third said they would have preferred a Grexit.

Mr Tsipras said he would defend his government from "the plans of certain conservative Europeans" and scoffed at the "Plan B" for the country's exit from the zone put forward by Germany's hawkish finance minister, saying "Europe does not belong to (Wolfgang) Schaeuble".