By Renee Maltezou and Robert-Jan Bartunek

ATHENS (Reuters) - Greece made last-minute overtures to its international creditors for financial aid on Tuesday, but it was not enough to save the country from becoming the first developed economy to default on a loan with the International Monetary Fund.

The left-wing Greek government had asked European partners for a two-year aid package to cover its financing needs. Later on Tuesday, Greece's Finance Minister Yanis Varoufakis indicated on a call with European counterparts that Athens might scrap a controversial July 5th referendum if a deal was reached, according to euro zone sources.

The flurry of diplomacy was an attempt to bring creditors back into talks after five months of inconclusive negotiations brought Greece close to leaving the euro currency bloc.

It came as tens of thousands of people descended on Athens' central Syntagma square over the past 24 hours in two different rallies - one to support the government and the other to push for Greece to remain in the euro.

Greece, as expected, was not able to repay 1.6 billion euros it owed to the International Monetary Fund, in what was the largest missed payment in the Fund's history.

Late on Tuesday, the IMF said it would examine a Greek request for a payment extension in due course.

The latest Greek proposals came too late to prevent Greece's existing aid package - with locked-up funds it needs to pay wages, salaries and debt - from expiring.

Still, in a sign that European officials have not given up on finding a solution for Greece, finance ministers said they would confer on Wednesday over Tsipras' latest loan request, effectively coming back to the negotiating table.

Sources said the officials are expected to discuss on Wednesday Greek Prime Minister Alexis Tsipras' request for the new two-year loan to pay debts that amount to nearly 30 billion euros. Tsipras is also seeking debt restructuring, an issue on which lenders have so far been reluctant to compromise.

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It was unclear how much the Wednesday call could achieve. Trust between Athens and European capitals is in tatters after acrimonious talks. The relationship further deteriorated after Athens on Saturday decided to put creditors' proposals for reforms in exchange for financial aid to a July 5th referendum.

The 40-year-old premier says the plebiscite is the democratic way for Greeks to say whether they will accept more budget cuts and taxes in order to maintain international aid. He has been urging people to vote against it, angering creditors.

German Chancellor Angela Merkel has ruled out further negotiations until after Sunday's referendum.

Jeroen Dijsselbloem, chairman of the euro zone's group of finance ministers, warned that Athens was welcome to ask for new aid but that it would come with conditions.

"What can change is the political stance of the Greek government that has led to this unfortunate situation," Dijsselbloem said.

In what appeared to be an effort to gain traction with his counterparts, Varoufakis indicated during the call late on Tuesday that Athens might call off the referendum or urge Greeks to vote in favor of bailout terms if a deal on a new loan was reached, according to euro zone sources.

A Greek official said that, as of late Tuesday, there were no changes in the planned referendum.

DEFAULT

Greece has received nearly 240 billion euros in two bailouts from the European Union and International Monetary Fund since 2010. The money has allowed the country to stay afloat but at a high cost to its population, which has swallowed many austerity measures such as cuts to pensions, wages and public services.

With its missed payment to the IMF, Greece is on a path out of the euro with unforeseeable consequences for both the EU's grand currency project and the global economy.

"What would happen if Greece came out of the euro? There would be a negative message that euro membership is reversible," said Spanish Prime Minister Mariano Rajoy, who a week ago declared that he did not fear contagion from Greece.

"People may think that if one country can leave the euro, others could do so in the future."

IMF Managing Director Christine Lagarde will immediately report to the global lender's board at close of business, Washington time, that Greece is "in arrears" - the official euphemism for default.

It is the first time in the history of the IMF that an advanced economy has defaulted on a loan from the world's financial backstop, putting Athens, which has seen its economy contract by more than 25 percent since 2009, in the same bracket as Zimbabwe, Sudan and Cuba.

Already the imposition of capital controls to prevent the crippled banking system from collapsing have given Greeks a bitter foretaste of the economic plunge that could follow exit from the euro.

Withdrawal limits of 60 euros a day have been fixed for cash machines and there have been long queues at petrol stations and in supermarkets as worried shoppers stocked up on essentials like pasta and rice.

There were no immediate signs of serious shortages but if the banks remain closed, cash flow problems which have already been reported by some firms, could worsen.

"So far there are no problems with suppliers, but if the banks are still closed next week there will be a bit of a problem if they demand purely cash payments," said Charisis Golas, owner of a small meat and dairy shop in Athens.

DEFIANCE

In Athens, opposition leaders - echoing EU officials - hammered home on Tuesday that the choice facing Greeks in the referendum is whether to stay in the euro zone or return to the drachma, even though the EU has no legal way of forcing a member state to give up the single currency.

Former Greek Prime Minister Antonis Samaras, leader of the main opposition party, said a "No" vote would push the country out of the single currency and wipe out wages and pensions.

The euro fell against the dollar but European shares, which dropped sharply on Monday, steadied on hopes of a deal. <.EU>. The Athens stock exchange is closed during a week-long shutdown of the banking sector which began on Monday.

Opinion polls show a majority of Greeks favor holding on to the euro, but the referendum is shaping up to be a close call.

(Additional reporting by Silvia Aloisi in Milan, Mark John in Paris, John O'Donnell in Frankfurt, Paul Day in Madrid, George Georgiopoulos and Lefteris Karagiannipoulos in Athens, Padraic Halpin and Gavin Jones; Writing by Paul Taylor, James Mackenzie and Alessandra Galloni; Editing by Janet Lawrence, Toni Reinhold)