Monday's Eurogroup meeting on Greek debt only lasted a few hours, ended without a concrete deal but embarked on a debate on debt relief for Greece.

Finance ministers of the 19-country eurozone bloc discussed Greece's latest debt package and the contingency mechanisms in case Greece veers off course, as well as held first-round discussions on Greek debt sustainability, Eurogroup President Jeroen Dijsselbloem told a press conference.

He said Eurogroup welcomed Greece's latest legislative move of approving an austerity package, adding it "should pave the way for the successful completion of its first bailout review."

Greece's austerity reforms are currently being scrutinized by international lenders. If it successfully completes the review, the country could unlock 4 billion euros (4.55 billion U.S. dollars) in savings and repay 300 million euros to the International Monetary Fund (IMF) and 2.3 billion euros to the European Central Bank next month.

Although Greek parliament approved a key package of austerity measures overhauling pension and hiking income tax on Sunday, Athens will have to implement more austerity measures if it fails to meet the annual primary surplus targets of 3.5 percent of GDP in the medium-term, according to a statement issued by the Eurogroup.

The ministers, for the first time, exchanged views on debt relief.

"The Eurogroup stands ready to consider, if necessary, possible additional debt measures aiming at ensuring that Greece's refinancing needs are kept at sustainable levels in the long-run," said the statement.

Dijsselbloem outlined a "three-layer" approach to tackle Greek debt relief on a short, medium and long-term basis.

In the short term, the Eurogroup will look for possibilities to optimize Greece's debt to lower repayment costs.

In the medium term, it asked working group to explore specific measures, such as prolonging repayment dates or lowering interest rate cost, in 2018 at the end of the current program.

In the long run, the Eurogroup stands ready, if necessary and if Greece complies with its targets, to consider whether further debt relief is needed, it said.

The Eurogroup's aim was to make Greek debt sustainable in the long term, Dijsselbloem said.

"It is a great relief that we are talking about debt and a great relief we are talking about specific," said Greek Finance Minister Euclid Tsakalotos after the meeting.

He said he supported the Eurogroup's "three-layer" approach and expected to have an agreement on fine-tuning the contingency measures by May 24, the deadline set by the Eurogroup to clinch a final decision.

"Both Greece and our creditors need to feel that we are turning the page and that the vicious circle of measures leading to recession, leading to new measures, is over," Tsakalotos said.

"Once we have the green light from creditors, it will give much-needed confidence to businesses, investors and consumers," he said.

International creditors are divided on Greece's bailout conditions. The IMF insisted that Greek debt was unsustainable and needed debt relief while the EU side was more optimistic.

The IMF was pleased that debt relief was discussed on Monday, according to Tsakalotos.

The debt-ridden Greek economy is forecast to shrink this year again, following the slight growth in 2014 that snapped six years of recession. The jobless rate remained around 25 percent in the country, the highest in the bloc.

Last year, International creditors agreed to give Greece an 86 billion euros bailout loan to avert its exit from the single currency.