Greek politicians reacted angrily on Tuesday to concessions Athens offered in debt talks and parliament's deputy speaker warned the proposals might by rejected, puncturing optimism that a deal to pull Greece back from the abyss might be sealed quickly.

Euro zone leaders welcomed Monday’s new budget proposals from Athens as a basis for further negotiations to unlock billions of euros in aid and avert a default that could trigger a Greek exit from the single currency area.

Stock markets also greeted the news positively, with European shares extending the previous session’s sharp rally and climbing to a three-week high on hopes of a deal. But the euro fell on fears the plan would struggle to win approval in Greek parliament.

Prime Minister Alexis Tsipras, who was voted into office in January on a pledge to roll back years of austerity, must keep his leftist Syriza party as well as his creditors onside for a deal to stick.

Outspoken Syriza parliamentarians voiced outrage at Tsipras’s offer to raise a range of taxes as well as pension and healthcare contributions, which threaten to further increase hardship on Greeks.

"I believe that this programme as we see it ... is difficult to pass by us," deputy parliament speaker and Syriza lawmaker Alexis Mitropoulos told Greek Mega TV.

“The prime minister first has to inform our people on why we failed in the negotiation and ended up with this result,” he said. “I believe (the measures) are not in line with the principles of the left. This social carnage ... they cannot accept it.”

Officials of the three institutions representing Athens' creditors - the European Commission, the European Central Bank and the International Monetary Fund - were analysing the Greek proposals intensively in Brussels to see whether the numbers add up to make Greek public finances sustainable.

The creditors may well come back and demand further savings or reform measures in the drive to clinch a deal on Wednesday evening, people familiar with the talks said.

If parliament fails to back a deal, Tsipras might be forced to call a snap election or a referendum that would prolong the uncertainty.

Athens urgently needs money to avoid defaulting on a €1.6 billion euro loan repayment due to the IMF next Tuesday.

Jitters over the risk of a default leading to capital controls have prompted savers to pull billions of euros out of Greek banks, forcing the European Central Bank to increase emergency lending to keep them afloat.

With Greece perilously close to bankruptcy, it is unclear whether lawmakers would ultimately pull the rug from under Mr Tsipras if he secures a deal.

"I believe the deal will pass parliament and will reconfirm the government's majority," Dimitris Papadimoulis, a Syriza lawmaker at the European Parliament, said.

“I do not believe that top Syriza lawmakers will want to be responsible for bringing down a five-month-old government and a prime minister who enjoys popular support of about 70 per cent.”

Opinion polls suggest most Greeks want to stay in the euro. Mr Tsipras can also likely count on support from opposition lawmakers, who want to secure Greece’s place in the euro, even though the government says it cannot continue unless its own lawmakers back any deal it brings to parliament.

"If (the government) does not have the parliamentary majority, it cannot remain (in power)," government spokesman Gabriel Sakellaridis said.

The ECB raised the ceiling on emergency liquidity Greek banks can draw from the country’s central bank for the fourth time in a week on Tuesday, a banking source said, declining to say by how much.

In its proposal, Greece pledged to lift the retirement age gradually to 67 and curb early retirement, but avoiding making concessions on some so-called “red lines” like direct pension cuts or a mooted tax hike on electricity.

Reuters