Greece cleared a crucial hurdle in its massive bailout programme on Monday as eurozone ministers promised to consider debt relief to Athens, which is already under pressure from the refugee crisis.

Bailout monitors from the EU and IMF will return to Greece as soon as Tuesday in an effort to complete a long-delayed review of the programme that could unlock rescue cash, European Economic Affairs Commissioner Pierre Moscovici said.

"I am very happy that mission chiefs are going to Athens as soon as tomorrow," Moscovici said after a meeting of the eurozone's 19 finance ministers in Brussels, taking place in parallel to an EU-Turkey summit on the refugee crisis.

Greek Prime Minister Alexis Tsipras secured Greece's third bailout, worth a staggering 86 billion euros ($95 billion), last July after six months of bruising negotiations that shook the EU and nearly saw Athens thrown out of the single currency.

Along with its debt crisis the Greek state is now overwhelmed by the arrival of around a million migrants in a year.

As refugees trek across Europe seeking new lives in Germany and elsewhere, the fresh crisis has increased the pressure on Athens' eurozone partners to soften their demands of Greek austerity.

Eurogroup chief Jeroen Dijsselbloem, who last year was one of Greece's harshest critics, said eurozone ministers would now address debt relief, meeting a key demand of the Greek government that has been resisted by its pro-austerity partners.

The EU forecasts that Greece's debt will soar to 185 percent of gross domestic product (GDP) in 2016 -- a level generally understood to be unsustainable.

"We have a longstanding promise that if the Greek government fulfils its commitments ... we will do what is necessary to make debt service manageable," said Dijsselbloem.

"Today... we made explicit that the discussion is on our table," the Dutch finance minister said.

- 'Sensible solution' -
The review of Greece's bailout has been delayed for months amid a rift between top EU and IMF officials over how strictly to hold the Greek government to the ambitious reform commitments made as part of its bailout.

Greek Finance Minister Euclid Tsakalotos said a "sensible solution" would be found, as he celebrated a clear victory in the handling of the country's bailout.

The IMF has "agreed to come back despite certain differences," said Tsakalotos after the talks.

"We look forward to discussions, closing in a timely manner the first review and having a discussion on debt," he said.

Greek Prime Minister Alexis Tsipras on Sunday accused the Washington-based IMF of employing "stalling tactics" and "arbitrary" estimates to delay a reforms review crucial to unlock further bailout cash.

The leftist PM said the global lender was bent on unfair cuts that failed to take into account the improved performance of Greece's economy.

But the IMF has also backed Greece in its battle to win debt relief, believing no economic programme would be credible without it.

The IMF has yet to officially sign onto the third bailout of Greece and is making its participation conditional on Athens fulfilling its commitments, as well as the eurozone allowing for debt relief.