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Greece's latest debt plan the "first real proposals in many weeks", the president of the European Council has said.
Donald Tusk's tweets will provide hope to those who fear Greek exit from the EU is imminent.
A resolution to the Greek debt crisis could be reached "later this week", the head of the Eurogroup has said.
Jeroen Dijsselbloem said proposals from the Greek government had arrived too late for an agreement today, but that finance chiefs would now properly assess the plans in the hope of reaching a deal later this week.
"The work can start immediately as far as we are concerned," he said.
"If necessary - and if all goes well, it will be necessary - the euro group will have another meeting later this week to hear from the final outcome of the talks with the Greek authorities."
Any agreement on a deal to stop Greece defaulting on its debts is increasingly unlikely to be made today, ITV News Europe Editor James Mates says.
Jeroen Dijsselbloem, the president of the Eurogroup, has said the Greek government sent the "wrong version" of its plan to tackle its debt crisis to creditors last night, according to ITV News Economics Editor Richard Edgar.
Christine Lagarde, the head of the International Monetary Fund (IMF), has arrived in Brussels for talks over the Greek debt crisis.
There must be a "viable" solution to Greece's debt crisis, the country's prime minister has said as he arrived for crunch talks with European leaders.
"This is time for a substantial, viable solution that allows Greece to come back to growth within the eurozone with social justice," Alexis Tsipras said as he arrived in Brussels.
Speaking alongside Mr Tsipras, European Commission president Jean-Claude Juncker said there had been progress but added: "We are not there yet".
Greece has to reach a deal with its creditors before a June 30 deadline to repay a 1.6 billion euro (£1.1 billion) loan from the International Monetary Fund (IMF).
Mr Tsipras's left-wing Syriza government has presented new proposals for tackling the crisis which have to be approved before it can gain access to vital bailout funds.
British holidaymakers have been told that their trips to Greece should go ahead despite the ongoing financial uncertainty surrounding the country.
The Association of British Travel Agents (Abta) said it did not expect to have to rebook customers to different destinations and that it was not aware of any plans to evacuate people from Greece.
Abta did advise visitors to Greece to take some euros in cash and to ensure they had appropriate travel insurance.
"At present we have no indication that holidaymakers will be disrupted, however as with all destination matters we will continue to monitor the situation and work with our members on any developments," a spokesperson said.
The Foreign Office's advice to Brits travelling to Greece has not changed since May 6 when it advised travellers to take more than one method of payment, and to take enough money to cover emergencies.
Eurozone leaders will begin 11th-hour crisis talks today in a bid to haul Greece back from the brink of bankruptcy.
Officials worked late into the night to draw up an acceptable deal ahead of a leaders' summit in Brussels.
Over the weekend, Greek Prime Minister Alexis Tsipras presented a new offer.
The details of the proposal have yet to be revealed, but it follows increasing pressure from creditors to make extra spending cuts and tax hikes to help meet their obligations.
The latest proposals from Greece to solve its debt crisis is a "good basis for progress", a senior European Commission official has said.
Taking to social media to welcome the development, Martin Selmayr - who is chief-of-staff to President Jean-Claude Juncker - said the news put the country in a good position to begin talks among other euro zone leaders later today.
He added, in German: "eineZangengeburt", which means a "forceps delivery", but gave no other clue as to what he meant.
Officials from the EU, Greece and other creditors have been working for several months to complete a deal releasing funds to Athens, as fears grow over the chances of the country running out of cash this month.
Latest ITV News reports
Greece has blinked first - but is it enough to save the country from bankruptcy?
Thousands of pro-euro demonstrators have gathered in Athens as negotiations appear to be moving Greece close to a bailout deal.