Greek Prime Minister Alexis Tsipras was holding meetings with his leftist party Tuesday as he faced the tough task of selling a new bailout deal that requires Athens to push through draconian reforms within two days.

Tsipras needs to secure backing for the deal from the Greek people, parliament and his radical Syriza party, which shot to power in January on the back of promises to end five years of bitter austerity under two previous bailouts.

In the agreement struck Monday with the eurozone to prevent Greece crashing out of the euro, the Greek parliament must pass sweeping changes to labour laws, pensions, VAT and taxes by Wednesday.

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 ($96 billion), its third rescue programme in five years.

"The Gordian Knot has been untied with painful and harsh negotiations," Greek Interior Minister Nikos Voutsis told reporters on Tuesday outside the parliament building.

He expressed confidence that Syriza party dissenters would be kept in line. He added that "the people trust Tsipras and the government" to cancel out the worst effects of the bailout terms with other policies, but did not elaborate.

Syriza's junior coalition partner, the nationalist Independent Greeks party (ANEL) was also holding an emergency meeting Tuesday to determine its stance. Leader Panos Kammenos, who is defence minister, has said his party would not approve the tough measures but would stay in the government.

In Washington, the White House hailed the deal on Greece as "a credible step" on the long path to economic growth and debt sustainability in the hard-up country.

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

The last-ditch deal is aimed at keeping Greece's economy afloat amid fears its cash-starved banks were about to finally run dry and trigger its exit from the single currency.

Many ordinary Greeks however are sceptical that the deal will bring about any improvement in their lives. Some expressed their anger on social media, where the Twitter hashtag #ThisIsACoup trended.

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

Haralambos Rouliskos, a 60-year-old economist, described the deal as "misery, humiliation and slavery".

The eurozone creditors "are trying to blackmail us," said Katerina Katsaba, a 52-year-old working for a pharmaceutical company.

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

"This agreement may pass with (opposition party) votes, but it will never pass the people," the head of a hardline Syriza faction, Energy Minister Panagiotis Lafazanis, said.

If Greece passes it, 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.

Despite strong opposition, Tsipras also yielded to a plan to park assets for privatisation worth up to 50 billion euros in a special fund.

Some 25 billion euros of the money in that fund will then be used to recapitalise Greece's cash-starved banks.

There is also a pledge to reverse laws brought in by the Syriza government that run counter to Greece's earlier bailout arrangements in 2010 and 2012.

The deal contains little mention of relieving a Greek debt mountain worth 180 percent of GDP -- a step recommended by the International Monetary Fund -- beyond a vague mention that it should be considered later.

The eurozone must now unite to tackle the immediate problem of finding funds to keep Greece afloat, as the bailout could take months to finalise.

Eurozone finance ministers at a meeting on Monday considered bridge funding to get Greece through coming weeks when it faces several huge debt payments to the ECB and other creditors.

"We have not yet found the 'golden key' to solve this issue," said Eurogroup head Jeroen Dijsselbloem, who was renamed to a second term at the minister talks on Monday.

Despite the deal, Greece missed a second debt payment to the IMF in two weeks on Monday, bringing its total arrears to the Fund to about 2.0 billion euros.

The ECB meanwhile has kept Greek banks afloat -- barely -- with emergency liquidity, but has refused to provide extra funds.

The ECB's governing council on Monday held its emergency liquidity assistance for Greece unchanged at around 89 billion euros ($99 billion).

Banks will stay closed in Greece until Wednesday, the country's finance ministry said in a statement.

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