On Tuesday Athens missed the deadline for a €1.5bn ($1.7bn) payment to the International Monetary Fund (IMF).
Greece no longer has access to billions of euros in funds, as the previous eurozone bailout expired.
IMF head Christine Lagarde said the fund would still try to help and that she hoped the referendum would bring "more clarity".
At a referendum to be held on Sunday July 5, the Greek will be asked to either accept or reject proposals made by creditors last week, with Prime Minister Alexis Tsipras urging a "No" vote.
Finance Minister Yanis Varoufakis said creditors are blackmailing Greece.
But he pledged a deal would be reached soon after the vote and that current limits on bank withdrawals would ease.
Earlier on Wednesday Mr Tsipras put new proposals to eurozone creditors, accepting most of what was on the table before talks with creditors collapsed last week, but with conditions.
His latest offer is tied explicitly to agreement on a request for a third bailout from the eurozone's bailout fund lasting two years and amounting to €29.1bn. However, Dutch Finance Minister and Eurogroup President Jeroen Dijsselbloem commented that a new bailout package could only be discussed "after and on the basis of the outcome of" the vote.
German Chancellor Angela Merkel insisted further negotiations are possible only after the outcome of the vote.
However, French President Francois Hollande said he wanted a deal to be found before the referendum.
The Greek authorities had to imposed capital controls over the weekend, and bank banks did not open this week after the European Central Bank blocked their liquidity lifeline, and on Wednesday decided to keep the emergency funding at the same level.
But the regulator did not decide to demand more collateral from Greek banks as some had speculated it might.
Cash withdrawals are now capped at just €60 a day but some bank branches reopened on Wednesday to allow pensioners - many of whom do not use bank cards - a one-off weekly withdrawal of up to €120, says BBC News.
Owners of the Greek debt (in euros)
Source: BBC News
Lenders' proposals, key points
- VAT (sales tax): Greek PM accepts a new three-tier system, but wants to keep 30% discount on the Greek islands' VAT rates. Lenders want the islands' discounts removed.
- Pensions: Ekas top-up grant for some 200,000 poorer pensioners will be gradually reduced 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
In the markets, EUR/USD was last at 1.1069 gaining 0.14%.
Overnight, U.S. stocks edged higher on the first day of trading of the second half of the year, ahead of Greece's referendum and of Thursday's release of the U.S. jobs report for June.
The Dow Jones Industrial Average and NASDAQ Composite each rose moderately, driven by gains in Apple Inc while the S&P 500 moved higher one session after ending a quarter in negative territory for the first time in more than two years.
