Greece formally requested a three-year bailout from the eurozone’s rescue fund Wednesday and pledged to start implementing some overhauls by the beginning of next week, according to a copy of the request seen by The Wall Street Journal.

The letter is a first step toward fulfilling a demand by international creditors to come up with tougher measures in return for desperately needed financing that could keep the country from bankruptcy and even worse economic turmoil.

The letter says Greece will put in place tax-reform and pension-related measures, though it doesn’t go into detail. Greek Prime Minister Alexis Tsipras said his government would present more concrete measures on Thursday by a midnight deadline.

The government in Athens has resisted implementing economic-policy overhauls and budget cuts. The impasse has held up a deal between the two sides for months, and raised the specter of an imminent Greek exit from the eurozone.

Key differences still remain. In his first address to the full European Parliament in Strasbourg, France, Mr. Tsipras mixed conciliation with defiance, pointing to his countrymen’s resounding “no” vote in Sunday’s national referendum as evidence he has a fresh mandate to demand a good deal for Greece.

Mr. Tsipras said his proposals would contain demands for a “genuine dialogue” on restructuring Greece’s huge debt load, which he said was necessary to give the country “light at the end of the tunnel.”

“We demand an agreement with our neighbors but one that gives a sign that we are in a long-lasting basis for exiting from the crisis,” he said.

The full list of overhauls and budget cuts is what will determine whether the application for a new rescue program will be approved by the rest of the eurozone. The currency union’s leaders will assess whether it makes sense to start formal negotiations on a bailout program at an emergency summit on Sunday.

German Finance Minister Wolfgang Schäuble’s spokesman said a comprehensive list of reforms is precondition for Germany to examine Greece’s bailout request, signaling Berlin wouldn’t bow to time pressure despite the deadline.

“The actual examination can only begin once the full package has been put on the table,” Martin Jäger said,

Mr. Tsipras indicated that it might be possible to reach an “effective and fair” compromise with Greece’s creditors, but he also criticized previous bailout deals that he said had saved European banks that had lent to Greece, and “never trickled down to ordinary men or women.”

Guy Verhofstadt, leader of the European Parliament’s liberal party grouping, urged Mr. Tsipras to come forward with “a credible reform package” that included a clear calendar and efforts to stamp out patronage.

“You are talking about reforms but we never see concrete proposals of reforms,” Mr. Verhofstadt said, in a speech that was greeted with loud applause.

Without some new cash in the coming weeks, Greece won’t be able to make a €3.5 billion ($3.8 billion) bond payment to the European Central Bank on July 20.

Such a nonpayment could push the ECB to cut emergency lending to Greek banks—a move that would send the country’s financial system into meltdown and force the government to print its own money to recapitalize them.

European shares rose on the news of the letter. The Stoxx Europe 600 rose 0.4% midway through the session, having oscillated between slight losses and gains during the morning.

The letter from Finance Minister Euclid Tsakalotos to Jeroen Dijsselbloem, the chairman of the Eurogroup of finance ministers, and Klaus Regling, the managing director of the European Stability Mechanism—the European bailout fund—overtakes a request from last week for a two-year rescue program.

The letter doesn’t carry Mr. Tsakalotos’s signature and ends with “Yours faithfully, Minister of Finance.” A previous request that has been voided by Wednesday’s letter had the signature of Mr. Tsipras. European officials didn’t immediately appear concerned about the lack of handwritten signature.

A spokesman for the fund confirmed it has received Greece’s request for a new loan.

In the letter, Greece said it would “honor its financial obligation to all of its creditors in a full and timely manner,” indicating that it hopes to meet the July 20 payment. It said that it the bailout loans would be used to “meet Greece’s debt obligations and to ensure the stability of the financial system.”

Finally, the letter also makes a request for debt relief, albeit in much more toned-down language than earlier demands. “As part of a broader discussion to be held, Greece welcomes the opportunity to explore potential measures to be taken so that its official sector related debt becomes both sustainable and viable over the long term,” the letter says.

Eurozone finance ministers won’t be discussing the request Wednesday as had been expected, said a spokesman for Jeroen Dijsselbloem, the Dutch finance minister who leads the discussions among his eurozone counterparts.

The request will be dealt with in a teleconference by senior officials from national finance ministries instead, he added in a message from his Twitter account.

Germany has opposed the Greek government’s bid for debt relief, though officials have suggested they might be open to the possibility if the government commits to overhauling its economy.

The IMF, Greece’s biggest creditor outside the eurozone, has long insisted that high debt has been weighing on growth and that the currency union’s governments should take action to reduce it. Wall Street Journal