(Updates with comment from Luxembourg finance minister)
By Renee Maltezou
ATHENS, May 4 (Reuters) - Prime Minister Alexis Tsipras called on Greece's international lenders on Thursday to reach an agreement on easing its debt burden by May 22, when euro zone finance ministers meet in Brussels to discuss the country's bailout progress.
Athens and its creditors reached a long-awaited deal at staff-level this week on a series of bailout reforms Greece needs to unlock loans from its 86-billion-euro rescue package, the country's third since 2010.
The European Union and the International Monetary Fund, which has yet to announce if it will participate in the bailout, have now started negotiations over Greece's post-bailout fiscal targets, a key element for granting it further debt relief.
Greece is being firm that it has done what was asked of it and now wants to see movement from the other side.
"Medium-term debt relief measures must be clearly defined by the May 22 Eurogroup meeting," Tsipras told his cabinet on Thursday, referring to the finance ministers. "Greece has done its part and all parties must now fulfil their commitments."
The creditors have been not been quite as upbeat and there is no guarantee that the May 22 meeting will actually sign off on the new tranche of loans, let alone draft up debt relief.
But Luxembourg Finance Minister Pierre Gramenga did cite progress when speaking to reporters on the sidelines of a conference in Luxembourg.
"We're one step closer. They (Greece) over-performed last year, they are on track this year, we have now an agreement looming that we will hopefully agree on in Eurogroup," he said.
"Those who have been pessimistic all the time have been proved wrong. I'm very pleased about that. The worst case is not always the scenario that plays out."
Greece's economy and budget have improved markedly recently, although major problems of poverty and unemployment persist.
An agreement on debt relief will help Greece wrap up its formal bailout review after six months of tense talks, help it qualify for inclusion in the European Central Bank's bond-buying programme, and let it return to bond markets.
Under discussion are the country's targets for a primary surplus - which excludes debt servicing costs - over a decade.
Tsipras' leftist-led government aims to legislate the recently-agreed reforms, which include cutting pensions in 2019 and reducing the tax-free threshold in 2020, by May 17.
The government, which faces elections in 2019 and is sagging in opinion polls, controls 153 lawmakers in the 300-seat parliament and should succeed. Labour unions have planned a 24-hour anti-austerity strike on the day of the vote.
"We decided to complete the process by May 17 in order to deprive the Eurogroup of the right to talk about delays and finding excuses to extend the discussions on debt relief," a government minister said after the cabinet meeting. (Additional reporting by Jamie McGeever in Luxembourg; editing by Jeremy Gaunt/Mark Heinrich)