Eurozone finance ministers hope to reach a deal on Greece's debt relief and release another tranche of bailout funds to the country in their June meeting, as they failed to reach an agreement on the matter with the International Monetary Fund on Monday.

Greek lawmakers approved a reforms package last Thursday that includes pension cuts and tax hikes as demanded by the country's creditors to pave the way for the disbursement of bailout funds totaling more than EUR 7 billion and to begin talks on debt relief.

Discussions over providing more bailout funds had stalled after a review mission to Athens returned in December without reaching a deal. The country is in dire need of bailout cash to meet debt repayment of more than EUR 7 billion due in July, or risk default.

Welcoming the progress made by Greece, Eurogroup President Jeroen Dijsselbloem said on Monday, "I think we are close to formally closing the second review, with a positive outcome."

That would open up discussion on debt sustainability, which was already explored in depth on Monday by euro area finance ministers and the IMF.

"At this point, we have not reached an overall agreement on that part of our discussion," Dijsselbloem said.

"We will try to come to an definite conclusion in the next Eurogroup meeting which will be in 3 weeks time."

The next Eurogroup meeting is scheduled to be held on June 15 in Luxembourg.

Greece has to implement 140 reform measures ranging from tax to privatization to secure funds and debt relief. The government must also adopt additional budgetary measures in 2019.

As of now, the country has completed 110 of the 140 measures, European Union Economic Affairs Commissioner Pierre Moscovici said.

There was a profound and detailed discussion on debt, he noted.

"We did not conclude but we advanced," Moscovici said. "We will now work to conclude a good deal on June 15th."

The IMF, which has sought debt relief for Greece, has stayed away from the latest bailout as it seeks assurance from the EU regarding the sustainability of the country's massive debt pile.

IMF's Head of the European Department Poul Thomsen said on Tuesday that both sides did make progress in debt talks, but "we are not quite there yet".

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