Euro zone finance ministers agreed on Friday to lend Greece up to 86 billion euros (61 billion pounds) after Greek lawmakers accepted their stiff conditions despite a revolt by supporters of leftist Prime Minister Alexis Tsipras.

Assuming approval by the German and other parliaments, 13 billion euros should be in Athens next Thursday to pay pressing bills and a further 10 billion will be set aside at the European Stability Mechanism, earmarked to bolster Greek banks' capital.

In all, euro zone governments will lend 26 billion euros in a first tranche of the bailout before reviewing Greece's compliance with their conditions in October.

One remaining uncertainty - aside from Tsipras' ability to deliver sweeping budget cuts and privatisations opposed by many of his own party - is the role of the International Monetary Fund. After backing two previous bailouts, the IMF renewed its call for the Europeans to grant Athens debt relief - a bone of contention between the Eurogroup and the Washington-based Fund.

Managing Director Christine Lagarde told the Eurogroup by telephone that she could not commit until the IMF board reviewed the situation in the autumn. Officials said the Fund needed more assurances and detail on Greek reforms, notably to pensions, and steps to persuade it that Greece's debt burden was sustainable.

But after deadlock since January that ravaged the already weak Greek economy and ended in a dramatic U-turn a month ago by the anti-austerity leftist government to avert Athens' expulsion from the euro, there was a cautious sense of optimism among ministers gathered in a Brussels deep in summer holiday languor.

"After six months of very difficult negotiations with lots of ups and downs, we finally have an agreement," Greek Finance Minister Euclid Tsakalotos told reporters. His appointment by Tsipras six weeks ago in place of his abrasive predecessor has been hailed by counterparts as a mark of a new Greek "realism".

"After the changes in the government and the crises that we had, the cooperation with let's say the changed Greek government is very constructive, very well organised," Jeroen Dijsselbloem, the Dutch minister who chaired the meeting, told reporters.

DEBT BURDEN

Even Germany's Wolfgang Schaeuble, who last month floated a Greek exit from the euro as Tsipras hesitated to agree terms with fellow leaders, sounded upbeat, if still wary of a new tone in Athens that caused an angry split in Tsipras' leftist party, with nearly a third of Syriza lawmakers rebelling in parliament.

"We will have to wait and see," said Schaeuble, who has become a hate-figure for rigid austerity among Greeks tired of five years of soaring unemployment. "This is an opportunity. But what is decisive is that Greece does what it says it will do."

Schaeuble was among numerous ministers who stressed they saw it as vital that the IMF take part in the third bailout, as it has in two programmes totalling 240 billion euros since 2010.

Not only would IMF lending reduce the amount needed from Europe - possibly by a sum similar to the 16 billion euros the Fund had ready when the second bailout programme expired - but the IMF's reputation for rigour would reassure sceptical parliaments and financial markets that conditions would be met.

Lagarde said in a statement that Europe would need to provide "significant" debt relief as a complement to reforms Athens is trying to put Greece's finances on a sustainable path.

"I remain firmly of the view that Greece’s debt has become unsustainable and that Greece cannot restore debt sustainability solely through actions on its own," she said, highlighting what has become a significant bone of contention with the European institutions with the IMF helped negotiate the new accord.

Led by Germany, euro zone governments have ruled out taking a "haircut" to reduce the nominal principle of Greece's debts to them. But the Eurogroup said in its statement that it would consider longer grace periods and repayment periods if Greece successfully met its loan conditions by an October review.

Dijsselbloem said it was still unclear that Greece could not afford to service its debts but he was optimistic differences with the IMF could be overcome. French Finance Minister Michel Sapin, among strong supporters of helping Greece stay in the euro zone, said that a consensus was emerging on the Greek debt.

Critics of past bailouts argue they can create a downward spiral as governments pump money out of the country to service foreign loans, choking domestic economic activity that generates the tax revenues the state needs to pay its debts. EU officials argue that Greece is borrowing already on very favourable terms.

While the broad outlines of the bailout agreement were set at a marathon, all-night summit a month ago and further filled in by negotiators who concluded a draft on Tuesday, euro zone ministers devoted some of their six-hour meeting to detailing a plan to recapitalise Greek banks. These have been ravaged by the uncertainty and by capital controls imposed in late June.

The agreement foresees up to 25 billion euros being set aside for bank capital, with 10 billion of that immediately and up to 15 billion by mid-November, after officials conduct stress tests of the banks' requirements. Shares issued by banks in return for capital are to be placed in a privatisation fund.

REVOLT IN ATHENS

After debating through the night, the Greek parliament gave its backing to Tsipras' plans to legislate what creditors want, though he had to rely on opposition votes after nearly a third of his own supporters rebelled, forcing him to consider a confidence vote that could pave the way for early elections.

After defeating conservatives in January, Tsipras remains hugely popular for standing up to Germany and he would be expected to win again, given an opposition in disarray.

A hardline faction in his party effectively gave notice it might break away, raising the prospect of Tsipras having to build a new, possibly unstable, coalition.

That could mean further uncertainty in Greece and in a wider euro zone economy which data on Friday showed still struggling to meet even modest growth expectations.

EU leaders say new measures to consolidate the euro zone mean threats to its survival are much weaker than when it first was hit by the global debt crisis. But German-inspired fiscal rigour despite continued high unemployment, especially among the young, continues to fuel opposition to European integration.

Nonetheless, Tsipras defended his abandonment of election promises he made to austerity: "I do not regret my decision to compromise," he told the parliament in Athens. "We undertook the responsibility to stay alive over choosing suicide."