The eurozone gave Greece its firmest offer yet of debt relief in what finance ministers called a breakthrough deal that won a commitment from the IMF finally to return to taking part in the bailout for Athens.

After talks that lasted into the small hours of Wednesday, the Eurogroup ministers gave a nod to releasing 10.3 billion euros ($11.4 billion) in new funds for Greece in recognition of painful fiscal reforms pushed through by Prime Minister Alexis Tsipras's leftist-led coalition, subject to some final technical tweaks.

But a bigger step forward was a deal by which the eurozone agreed to offer Athens debt relief in 2018 if that is necessary to meet agreed criteria on its payments burden. That was enough to secure an agreement from the International Monetary Fund to again join the euro zone in funding the bailout of Greece.

"We achieved a major breakthrough on Greece which enables us to enter a new phase in the Greek financial assistance program," Eurogroup President Jeroen Dijsselbloem, the Dutch finance minister, told a news conference. "This is stretching what I thought would have been possible not so long ago."

Acknowledging the "political capital" European ministers invested to reach the deal -- a nod to strong German objections to debt relief -- Dijsselbloem called it a "new phase" in a six-year drama to stabilize Greece's finances that has taken the 16-year-old eurozone to the brink of break-up.

Mutual trust was returning to the talks, he said, nearly a year after Tsipras's rejection of austerity measures pushed Athens close to be pushed out of the euro.

GREEK OPTIMISM

"I think there is some ground for optimism that this can be the beginning of turning Greece's vicious circle of recession-measures-recession into one where investors have a clear runway to invest in Greece," Tsipras's finance minister, Euclid Tsakalotos, told reporters as he left the Brussels meeting.

The IMF has long insisted on the European governments taking a hit to relieve Athens of some of its debt in order to make its public finances more sustainable. The refusal of Germany and others to do that had led to months of wrangling with the IMF in which Athens had been something of a spectator in negotiations.

While the Europeans did not offer immediate debt relief, or make an unconditional promise of reducing the payments Greece must make to them, they did spell out criteria for it. Athens' gross financing needs to be kept below 15 percent of GDP in the medium term and below 20 percent beyond that.

"The Eurogroup agreed today on a package of debt measures which will be phased in progressively, as necessary to meet the agreed benchmark on gross financing needs," a statement said.

IMF ON BOARD

The IMF's European director Poul Thomsen said he believed the measures would "deliver the necessary debt relief", though he cautioned that it was still up to the IMF board in Washington to determine whether to agree with his assessment. The extent of debt relief that would take place was still not clear, he said.

"It will deliver debt sustainability according to our standard criteria," Thomsen said, insisting that the IMF had not eased its insistence that it would lend more to Athens unless its European creditors ease its debt burden. "I do not see this as a weakening of the debt relief proposals," he said.

But he acknowledged that the Fund made a big concession by agreeing that the debt relief would only be finally decided in 2018, rather than up-front, as was the IMF's initial position.

The easing of Greece's debts could be achieved by various methods, including extending some maturities, the eurozone agreed -- not through a 'haircut' on the nominal debt.

Germany has been insistent that the IMF should take part in the bailout because the Fund's reputation for fiscal rigor, but it has also resisted demands from Washington for debt relief -- a move that Berlin fears would create a "moral hazard", giving eurozone debtors an incentive to break with austerity reforms.

Hardline Slovak Finance Minister Peter Kazimir, who has long been skeptical of help for Greece, said: "It was a complicated birth tonight. It's probably about as good as it gets."

Socialist French Finance Minister Michel Sapin heaped praise on Tsipras for pushing painful reforms through parliament in order to unlock a first tranche of new money worth 7.5 billion euros next month, with another 2.8 billion to come.

"Even if the discussions were long, the atmosphere was always extremely relaxed," he said. "This deal is first and foremost a declaration of confidence in today's Greece."

Before the meeting, Finance Minister Wolfgang Schaeuble told reporters he was not willing to commit to any action after next year, when Germany holds parliamentary elections in the autumn.