Greece and its creditors have agreed on some aspects of a deal to unlock urgent bailout aid, but differences remain on its soaring debt and the amount of fiscal pain the country will have to swallow—suggesting hard political choices are imminent for both sides.

Greek Prime Minister Alexis Tsipras said Thursday that his government could endorse the budget targets sought by its main creditors—other eurozone countries and the International Monetary Fund—but not their methods for hitting those targets, which include demands for pension cuts and heavy sales-tax increases.

Still, in a sign that Greece now thinks a deal can be reached soon, the government decided on Thursday to bundle its loan repayments to the IMF this month into one payment. Athens had previously rejected this option, even though it relieves pressure on its cash flow, for fear of signaling that it had no money. Instead, Greek officials had said they would bundle the IMF payments only if they were confident that a deal with creditors was near.

The tough economic-policy terms demanded by Greece’s creditors pose a severe dilemma for Mr. Tsipras. He must steer between Greek voters’ wish to avoid default and stay in the euro, and his left-wing Syriza party’s opposition to further austerity measures, especially ones that hit its lower-income supporters.

After days of intense talks between Mr. Tsipras and European and IMF leaders, the focus of the drama could soon shift to Athens, where Mr. Tsipras risks a revolt by Syriza’s left-wing hard-liners if he tries to impose the lenders’ terms. The prime minister called a parliamentary session for Friday to brief lawmakers on the negotiations.

German Chancellor Angela Merkel, who has orchestrated a push in recent days to make Greece accept onerous economic overhauls in return for new financing, cautioned that much work remains to be done to reach a deal. “The talks are ongoing,” she said Thursday. “But they are still far from having reached a conclusion.”

Ms. Merkel held a conference call with Mr. Tsipras and French President François Hollande later in the evening. “All sides showed willingness to find a solution,” a Greek official said.

At Ms. Merkel’s initiative, lenders this week presented Mr. Tsipras with the outlines of a final deal, saying it includes the minimum of fiscal measures and broader economic overhauls that Greece must carry out to earn further aid. The eurozone and IMF can ease terms of the offer only marginally, European officials said Thursday. Otherwise, Greece’s budget deficits would be too big to bring its debts under control.

IMF chief Christine Lagarde signaled Thursday that rendering Greece solvent would still require some form of debt relief from eurozone governments, meaning that tough bargaining would be needed between the fund and Europe, as well as between lenders and Athens. Still, some officials involved in the talks said the IMF had indicated to Europe this week that it wasn’t insisting on explicit promises of debt relief immediately, so as not to scuttle a deal on short-term financing.

The IMF is “flexible in assessing the measures that contribute to the fiscal targets that have been proposed,” Ms. Lagarde said. “But clearly, if there was to be slippages from those targets, for the whole program to add up, then financing has to be considered,” she said, adding that “financing” included the maturities and interest rates on Greece’s outstanding loans from Europe. Outright debt forgiveness is political anathema in Germany and some other European creditor countries, where the five-year-old, €245 billion ($274 billion) bailout program for Greece is controversial and Athens has been seen as dragging its feet on hard but necessary economic reforms.

The Syriza-led government, with its often confrontational rhetoric against Germany and other lenders, has struggled to drum up much sympathy around Europe for the pain of many Greeks as the country’s economy contracted by around 25% in the past seven years. Mr. Tsipras now finds himself caught between his lenders’ impatience for more overhauls and belt-tightening, and his society’s exhaustion under a bailout program that many economists say was flawed in both design and execution.

Greek and IMF officials said the Athens government had notified the fund that it would repay all four of its IMF loans that expire this month at the end of June, instead of on separate, scheduled dates starting Friday. IMF rules allow countries to bundle their loan repayments in this way, but the option has been used only once, by Zambia in the 1980s.

Bundling this month’s roughly $1.7 billion of IMF repayments into one payment on June 30 temporarily relieves some of the pressure on Greece’s coffers, allowing more time to negotiate a deal. Until Thursday, Greece had rejected the option of bundling its repayments for fear that such a move might communicate that it had run out of cash, potentially spooking Greeks and accelerating deposit flight from Greek banks.

Yet despite convergence in recent days, after four months of near stalemate, the talks between Greece and lenders remain thorny and differences deep, officials involved say. European officials say the big unknown is how far Syriza lawmakers are willing to go to reach an agreement that breaks their antiausterity election promises. Mr. Tsipras’s ruling coalition between Syriza and the right-wing nationalist Independent Greeks has a slender majority of only 12 seats in Greece’s 300-member parliament.

A negotiation between Mr. Tsipras and European Commission President Jean-Claude Juncker in Brussels on Wednesday night was “combative,” according to an official familiar with the meeting.

The IMF and the eurozone want the Greek government to achieve budget surpluses, excluding interest, of 1% of gross domestic product in 2015, 2% in 2016, 3% in 2017 and 3.5% in 2018. Those targets are lower than had been foreseen under Greece’s bailout program previously. But they are still higher than the Greek government wanted, and would require more spending cuts and tax increases that would further hit Greece’s deeply depressed economy. Remaining disputes center on which belt-tightening measures are needed to hit the targets.

Mr. Tsipras rejected proposals for further cuts to pensions and increases to value-added tax, which creditors insist are central to bringing Greece’s finances onto a sustainable path, according to Greek and European officials. But Mr. Tsipras also indicated some flexibility, raising lenders’ hopes that he would make further concessions, some officials said.

A revolt by Syriza hard liners that robs the premier of his majority could lead to new elections, a referendum, or a change of governing coalition, analysts and European officials say.

Some German officials say such political upheaval might prove unavoidable if Mr. Tsipras is to gain the political leeway to push through a deal.

Some Syriza officials say elections would be needed if the creditors maintained their hard line. “If our lenders want full surrender, they won’t have it,” deputy shipping minister Theodoros Dritsas told Greek television on Thursday. “If Europe goes crazy, then the Greek people can decide.”

Despite the tensions, many European officials say they are growing more confident that a deal can be struck that keeps Greece afloat and in the euro. “The next hours, the next days…are absolutely essential,” said Pierre Moscovici, the European Union’s economics commissioner. “I would say I’m optimistic.”