The leaders who met in Berlin agreed to work with "real intensity" to try to wrap up the negotiations in the coming days and to keep in touch with each other and with Tsipras.
Their meeting showed that national and international leaders have now taken the battle to keep Greece in the euro zone into their own hands after months of insisting it was a matter for technical negotiations among experts.
Failure to reach agreement this month could trigger a Greek default and lead to the imposition of capital controls and a potential exit from the euro zone, dealing a blow to Europe's supposedly irreversible single currency.
A Greek government official said Athens would make a 300 million euro ($329.58 million) repayment to the IMF on Friday as due if there was an agreement with the creditors, hinting it might otherwise withhold the money without saying so explicitly.
"If we judge that a deal has been sealed, then we will make the June 5 payment normally," the official said, adding that the money would be transferred if there was a preliminary agreement that was not yet approved by Eurogroup finance ministers.
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EU Economy Commissioner Pierre Moscovici said the talks were making progress at last, citing what he said were new Greek proposals on pensions, a core issue for the creditors, who are demanding some benefit cuts and a crackdown on early retirement to make the complex system financially sustainable.
Greek officials played down talk of new pension proposals.
"Greece has been flexible for a long time on pension reform, willing to scrap incentives for early retirement and proceed with merging pension funds.
This is what is still on the table," a Greek government official said.
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Greece's central bank governor, Yannis Stournaras, who served as finance minister in a previous conservative-led government, urged the government to respect the "sacrifices" its people had made to stay in the euro, citing a 35 percent drop in living standards during the crisis that began in 2009.
Moscovici deflected Greek demands for official debt relief, saying the issue of making Greek debt sustainable in the longer term would only be addressed once Athens had accepted a cash-for-reform deal to release some 7.2 billion euros in frozen aid.
That programme expires at the end of June unless there is an agreement.
The ECB's top banking supervisor, Daniele Nouy, stressed on Tuesday that Greece's banks remain solvent despite deposit outflows and the government's cash squeeze - a key condition for the central bank continuing to provide emergency liquidity.