ATHENS, Greece (AP) — Greece's government has made new concessions in talks with its creditors, though some European officials said they were still not good enough and that a deal was nevertheless impossible before a Greek referendum on Sunday.

Prime Minister Alexis Tsipras sent a letter Tuesday night, just hours before the country's bailout program was due to expire, saying his government was prepared to accept creditors' proposals made last weekend, subject to certain amendments.

The creditors did not accept Greece's new overture, leaving the country's bailout program to expire. But eurozone finance ministers will meet again on Wednesday to discuss the terms again. Hopes that Tsipras was softening his position — after refusing for five months the spending cuts that creditors had demanded in exchange for loans — boosted markets on Wednesday.

But German Finance Minister Wolfgang Schaeuble was clear that no deal was imminent, at least not before Greece holds a popular vote on the creditors' proposals on Sunday.

"Before a referendum, there is indeed no basis (for an agreement)," Schaeuble said.

In Athens, crowds of anxious elderly Greeks thronged banks for hours from before dawn Wednesday, struggling to be allowed to withdraw their maximum of 120 euros ($134) for the week after the government reopened some banks to help pensioners who don't have bank cards.

Greece is in a financial limbo now that its bailout program has expired, cutting it off from vital financing and pushing it one step closer to leaving the euro. The country has put limits on cash withdrawals in order to keep banks from collapsing.

Its situation was further worsened Tuesday when it failed to repay a debt to the International Monetary Fund, the first developed country to do so. The last country to miss an IMF payment was Zimbabwe in 2001. As long as it is in arrears on the payment to the IMF, one of the country's main creditors, Greece cannot get any more money from the organization.

Greece's crisis took a turn for the worse after Prime Minister Alexis Tsipras announced last weekend that he would put a deal proposal by Greece's international creditors to a referendum on Sunday, July 5, and urged a "No" vote.

The move increased fears the country could soon fall out of the euro and saw Greeks rushing to pull money out of ATMs, leading the government to shutter its banks and restrict banking transactions. Greeks are now limited to ATM withdrawals of 60 euros ($67) a day and cannot send money abroad or make international payments without special permission.

European officials and Greek opposition parties have been adamant that a "No" vote on Sunday will mean Greece will leave the euro and possibly even the EU. The government rejects the argument as scaremongering, and says dismissing creditor demands will mean the country is in a better negotiating position.

However, government officials have begun hinting that the referendum might not go ahead if agreement with creditors is reached this week.

"Look, if a deal is found, there is a chance there could be this possibility too. Everything is developing," Health Minister Panagiotis Kouroumplis said when asked during a morning news show on Antenna television whether the referendum could be called off under certain circumstances.

On Tuesday night, Deputy Prime Minister Yannis Dragasakis hinted the same. The government decided on the referendum, he said on state television, "and it can make a decision on something else."

It was unclear, however, how that would be possible as Parliament has already voted for the referendum to go ahead.

With many elderly Greeks unable to access any money without bank cards, the government said about 1,000 bank branches across the country would open for three days starting Wednesday to give them access to some cash.

But a seeming last minute decision to serve customers on an alphabetical basis, announced by some banks overnight and by others in the morning, led to chaotic scenes of confusion and anger, with many pensioners waiting for hours from before dawn to be eventually told they would have to return Thursday or Friday.

Others were told their pensions had not yet been deposited and they would therefore have to return later in the week.

"It's very bad," said retired pharmacy worker Popi Stavrakaki, 68. "I'm afraid it will be worse soon. I have no idea why this is happening."

Meanwhile, many ATMs had run out of 20 euro notes, meaning the maximum they would dispense per day was one 50 euro note per bank card, effectively cutting the amount of cash Greeks have access to.

Capital controls will remain in place until at least next Monday.

"I don't have a lot of money, but I have to buy medicine. It's important," said 62-year-old Nikolaos Agonatos.

Greece's latest offer involves a proposal to tap Europe's bailout fund — the so-called European Stability Mechanism, a pot of money set up after Greece's rescue programs to help countries in need. It does not include the IMF.

Tsipras' office said the proposal was "for the full coverage of (Greece's) financing needs with the simultaneous restructuring of the debt."

Speaking on a late-night television interview Tuesday, Dragasakis said the new proposal "narrows the differences further" between Athens and its creditors.

"We are making an additional effort," he said. "There are six points where this effort can be made. I don't want to get into specifics. But it includes pensions and labor issues."

On international markets, shares in Japan and Hong Kong rose slightly Wednesday as investors watched to see the next step in the Greek saga.

"International markets appear to have found a level where they are happy to sit and wait on the next developments in the Greek debt crisis. Greece's failure to meet the deadline on its IMF payment looks to have been fully anticipated by markets. Barring unknowns, the next critical event for markets will be the outcome of Sunday's referendum," Ric Spooner, chief market analyst at CMC Markets, said in a commentary.

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Gregory Katz in Athens contributed to this report.