ATHENS (Reuters) - New ministers in Greek Prime Minister Alexis Tsipras' governmentwere sworn in on Saturday after a reshuffle expelled dissidents from his cabinet and began a new phase of negotiations for a third bailout package.

Tsipras sacked hardline former Energy Minister Panagiotis Lafazanis and two deputy ministers on Friday in a change that marked a split with the main leftist faction in the ruling Syriza party following a rebellion over the bailout terms.

Panos Skourletis, a close Tsipras ally who left the labor ministry to take over the vital energy portfolio, said the reshuffle marked "an adjustment by the government to a new reality".

The deal, approved with the support of opposition parties on Thursday after 39 Syriza rebels withheld their backing, agrees a painful mix of tax hikes, spending curbs and pension cuts as well as a rollback of collective bargaining agreements.

In addition, 50 billion euros ($54.14 billion) in public assets are to be placed in a special privatization fund to act as collateral for loans of up to 86 billion euros that must now be agreed with European partners.

In place of the rebels, Tsipras named allies of his own or his junior coalition partners, the right-wing Independent Greeks party, aiming to seal the bailout accord with European partners over the next few weeks before likely new elections.

"Our aim is to negotiate hard for the terms of the agreement, not just to seal it, but on how it will be implemented. There are many vague terms in the text," said newly-appointedLabor Minister George Katrougalos.

He said the government, elected in January on an anti-austerity platform, would fight for an agreement that was "socially just" and dismissed suggestions that it would have to take on the powerful labor unions and risk street protests.

"The Left is with demonstrations. The Left wants the people on the streets," he said.

Acceptance of the tough bailout terms marked a turnaround for Tsipras after months of acrimonious talks and a referendum that resoundingly rejected a less stringent deal proposed by the lenders. But opinion polls suggest the prime minister's own popularity remains high.

A poll published on Saturday in the leftwing Efimerida Ton Syntaknon newspaper suggested Syriza would get 42.5 percent of the vote if an election were held now, almost double conservative New Democracy's 21.5 percent.

In addition, 70 percent said they would prefer to accept the bailout deal if it kept Greece in the euro.

Negotiations on the package are set to begin from next week after parliaments in Germanyand other European countries gave their asset and European authorities approved emergency funding that should enable Athens to avoid defaulting on a 3.5 billion euro debt repayment due on Monday.

The European Central Bank has also agreed to release 900 million euros in emergency credit next week to the stricken Greek banking sector. But banks remain closed until at least Sunday and it is still unclear whether they will be able to reopen immediately.

(Writing by James Mackenzie; Editing by Tom Heneghan)