Greece's Prime Minister Alexis Tsipras has offered new concessions to the country's creditors.
In a letter to creditors, he said he was prepared to accept most conditions that were on the table before talks collapsed and he called a referendum.
Speaking on Greek TV, he once again urged a "No" vote in Sunday's poll.
Germany says talks on a new bailout to replace one that ran out on Tuesday will not be possible until after the referendum this weekend.
Human rights body the Council of Europe has said the referendum, which will ask Greeks if they want to accept their creditors' proposals, would "fall short of international standards" if held as planned on Sunday.
The body's Secretary General Thorbjorn Jagland told AP that the fact the vote "has been called on such a short notice... is a major problem", and criticised the lack of clarity in the question to be put to voters.
In his address on Wednesday Mr Tsipras thanked Greeks for their "calm" in the face of bank closures and said their salaries and pensions would "not be lost".
He angrily denied he had a secret plan to take Greece out of the euro, calling those who accused him of this "liars".
The letter sent to creditors by Mr Tsipras says he was prepared to accept a deal put forward last weekend, if a few changes were agreed.
European markets surged on the news Greece might be willing to accept a deal.
But the German Chancellor, Angela Merkel, said no new bailout talks would be possible before Greece holds Sunday's referendum.
The BBC's Europe correspondent Chris Morris says that as well as seeking further amendments to the creditors' proposals, Mr Tsipras's latest offer is tied explicitly to agreement on a request for a third bailout lasting two years and amounting to €29.1bn.
In other words, Mr Tsipras is attaching new conditions to any agreement on economic and structural reforms, our correspondent says.
And his application for a third bailout was accompanied by a request for debt restructuring that other eurozone countries would, at this stage, be unwilling to consider, he adds.
Lenders' proposals - key sticking points
- VAT (sales tax): Alexis Tsipras accepts a new three-tier system, but wants to keep 30% discount on the Greek islands' VAT rates. Lenders want the islands' discounts scrapped
- Pensions: Ekas top-up grant for some 200,000 poorer pensioners will be phased out by 2020 - as demanded by lenders. But Mr Tsipras says no to immediate Ekas cut for the wealthiest 20% of Ekas recipients
- Defence: Mr Tsipras says reduce ceiling for military spending by €200m in 2016 and €400m in 2017. Lenders call for €400m reduction - no mention of €200m
Two key meetings are to take place to discuss aid for Greece, after Athens missed the deadline for a €1.5bn (£1.1bn, $1.7bn) payment to the IMF on Tuesday.
Eurozone finance ministers were due to discuss Greece's new proposal in a conference call at 15:30 GMT.
The second meeting will see officials with the European Central Bank (ECB) deciding on whether to demand more collateral from Greek banks on emergency loans it has given them.
With the previous eurozone bailout expired, Greece no longer has access to billions of euros in funds.
Only three other countries are still in arrears to the IMF - Sudan, Somalia and Zimbabwe. Between them, they owe €1.6bn, only marginally more than Greece.
The ECB has also frozen its liquidity lifeline to Greek banks, which did not open this week.
Withdrawals from cash machines are capped at just €60 a day and long queues have been forming outside banks.
However, up to 1,000 branches re-opened on Wednesday to allow pensioners - many of whom do not use bank cards - a one-off weekly withdrawal of up to €120.
The Associated Press news agency said many pensioners had waited outside banks from before dawn, only to be told to return on Thursday or Friday.
Some pensioners were told their pensions had not yet been deposited, AP said.
"It's very bad,'' said Popi Stavrakaki, 68. "I'm afraid it will be worse soon. I have no idea why this is happening."
Close to 300 pensioners marched on the Bank of Greece in Athens after being given only a small sum from banks in the morning instead of the entire €120.
The European Commission - one of the "troika" of creditors along with the IMF and the ECB - wants Athens to raise taxes and cut welfare spending to meet its debt obligations.
Greece's left-wing Syriza government, elected on an anti-austerity platform, has been in deadlock with its creditors for months over the terms of a third bailout.
Last weekend, the Greek government took the unilateral decision to hold a vote, angering eurozone ministers.
EU leaders have warned that a "No" vote would see Greece leave the eurozone - though Mr Tsipras says he does not want this to happen.
A poll by the Greek newspaper Efimerida ton Syntakton published on Wednesday suggested that 54% of Greeks would vote against the creditors' terms for a bailout - but that the number of "No" voters had fallen since the introduction of capital controls.
Greece's cash trap - Dimitris Katsikas, Hellenic Foundation for European and Foreign Policy
The economy is frozen and we're in a liquidity trap, where everyone wants to hold euros.
Investment is non-existent and consumption has collapsed.
People have stopped submitting tax income statements and with the banks closed the government cannot receive anything. Supermarkets don't know what to do with the cash they receive.
We are not in the eurozone bailout programme so the European Central Bank cannot increase funding to the banking system.
Credit agencies have reduced the ratings on Greek banks so they're almost junk and even if they have collateral to give they may not be able to get new funding. Plus, we are essentially in default of the IMF.
Even if there is a deal, capital controls will be here for some time because there would be a rush on the banks if they re-opened.
An interim solution would only calm the symptoms of the crisis. Under a more permanent deal difficulties would remain for some weeks.
What happens next?
1 July - Eurogroup - the finance ministers of the eurozone - holds a telephone conference to discuss new proposal from Greek Prime Minister Alexis Tsipras
5 July - Referendum on creditors' proposals takes place, which many say is effectively a vote on Greek membership of the eurozone
20 July - Greece must redeem €3.46bn of bonds held by the European Central Bank. If it fails to do so, the ECB can cut off Greece's access to emergency loans
Are you in Greece? What are your concerns? Do you have friends and family in the country who may be affected? Email email@example.com with your experiences.
If you would be happy to speak further to a BBC journalist, please include a contact telephone number. You can also tweet your stories to @BBC_HaveYourSay or text 61124. If you are outside the UK, send them to the international number +44 7624 800 100.
Or WhatsApp us on +44 7525 900971
Read our terms and conditions.