Eurozone pioneers have resounded trusts that an arrangement can be struck inside of days to stop Greece defaulting on its obligation.
German Chancellor Angela Merkel said new recommendations offered by Greece constituted "some advancement". However, she said more work was required and "time is short".
Greece must reimburse a €1.6bn (£1.1bn) International Monetary Fund (IMF) credit before the month's over.
On the off chance that it neglects to do as such, it dangers smashing out of the single money.
BBC Europe Correspondent Damian Grammaticas, in Brussels, says that albeit no arrangement has been struck, the blockages on a route to an arrangement seem to have been cleared.
Prior, Greece's economy clergyman laid out new duties on organizations and the affluent that he trusted would break a halt with leasers.
The move was gotten with mindful hopefulness by pioneers of 18 other eurozone countries accumulated for a crisis summit in Brussels.
Greek Prime Minister Alexis Tsipras met the leaders of Greece's three worldwide loan bosses - the IMF, the European Commission and the European Central Bank (ECB) - in Brussels on Monday in front of going to the summit.
After the discussions finished on Monday evening, Mrs Merkel said that everybody joining in needed Greece to stay in the eurozone, "myself included".
"The proposition offered by Greece today constitute some advancement. In any case, it turned out to be clear amid our exchanges that there is a great deal of work to be done and time is short. Furthermore, thusly we have to work with full fixation," she said.
French President Francois Hollande, who likewise went to the discussions, said Greece and its lenders were "moving towards an accord".
He likewise said there was "still work to be done" for an answer for be "in sight" when eurozone fund priests meet again on Wednesday.
European Council President Donald Tusk portrayed the new Greek recommendations as "a positive step".
"Executive Tsipras has guaranteed us of Greece's reality and ability to work helpfully," he said.
"As the most recent hours have indicated we can see all gatherings completely dedicated to discovering an answer. The new Greek proposition to the three foundations are a positive stride forward as indicated by the introductory evaluation of the establishments. They will be further evaluated over the advancing hours."
He said the point was to have eurozone account priests affirm a bundle on Wednesday evening that would be put to eurozone pioneers for last underwriting on Thursday morning.
European Commission President Jean-Claude Juncker - one of the key force specialists - told a late-night news meeting: "I am persuaded that we will go to a last understanding throughout this week".
Talks have been in halt for five months with Greece's three fundamental banks unwilling to open the last €7.2bn tranche of bailout trusts until Greece consents to financial changes.
Greece's left-wing Syriza government has contradicted changes that it says will force pointless hardship on the Greek individuals.
Prior on Monday, Greece's economy clergyman Giorgios Stathakis said the new proposition included new charges on business and the affluent yet no further cuts in benefits or open part pay rates.
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