By Matthew Karnitschnig in Berlin and Gabriele Steinhauser in Brussels 

Greece and its creditors veered toward confrontation as its new, leftist government pledged to make good on promises to reverse years of public-spending cuts despite warnings from Berlin and other European capitals that doing so could plunge the country, and Europe, into deeper crisis.

Europe's political establishment sought to show respect for the will of the Greek people on Monday while also swiftly moving to douse hopes in Athens that it would substantially relax the country's bailout terms, which many Greeks blame for their economy's deep malaise.

"There are rules, there are agreements," German Finance Minister Wolfgang Schäuble said of the framework for Greece's financial rescue. "Whoever understands these things knows the numbers, knows the situation."

Europe's resolute response is driven in part by concern that such a step would invite other bailout recipients, including Portugal and Ireland to demand similar concessions and further erode the eurozone's credibility.

"If we start playing this game of 'the more radical you are, the more debt we're going to forgive you,' we're simply opening the door to have the European Union dismembered," said Esteban Gonzalez Pons, head of Spain's Popular Party in the European Parliament, adding that the eurozone was fully prepared to withstand a possible Greek exit.

Those opposed to relaxing the burden also worry that the electoral success of the leftist Syriza party, which surpassed many expectations, could energize other populist movements elsewhere in Europe.

Fresh from its first-place finish in Sunday's election, Syriza signaled it would stick to its strong antiausterity approach, forging a coalition with the Independent Greeks, a small right-wing party. The two coalition partners have little in common except opposition to European policies requiring tough fiscal rigor and sacrifice in exchange for financing to keep the debt-ridden country solvent.

Alexis Tsipras, the leftist firebrand who was sworn in as Greece's new prime minister on Monday, said he would give his all "to protect the interests of the Greek people."

The rhetorical jockeying underscores the challenges facing European and Greek leaders in the weeks ahead. The gulf between the new governing coalition and the country's European creditors is so wide that some policy makers see a Greek exit from the euro as a possibility in the coming months.

Syriza surged to victory on Sunday by promising Greeks that it would reverse many of spending cuts and labor-market reforms that Athens's creditors have demanded of it in return for aid. Mr. Tsipras also has also called for Greece's creditors--a group that includes the European Central Bank, other European Union countries and the International Monetary Fund--to forgive about one-third of the country's more than EUR300 billion ($338 billion) in debt.

Greece has little time to resolve the impasse. Europe's participation in Greece's EUR240 billion bailout program expires at the end of February. To receive the final EUR7.2 billion chunk and pay the ECB billions of euros in bond redemptions this summer, Greece must implement further reforms demanded by its so-called troika of overseers, the European Commission, the ECB and the IMF.

Both a reversal of Greece's reform agenda and large-scale debt relief are anathema to Germany and a number of other EU countries.

Asked in Brussels whether Greece could expect Europe to restructure its debt, the head of the currency's bloc's conference of finance ministers, Jeroen Dijsselbloem, was blunt: "I don't think there is a lot of support for that in the eurozone," he said.

Mr. Dijsselbloem said the bloc had already acted to relieve the pressure on Greece by reducing interest on its debt and extending maturities. Some officials have hinted they might be open to further interest-rate cuts and repayment extensions but only in return for continued reforms, a course Syriza has so far rejected.

Much of Europe's debate over Greece focuses on whether the country deserves even more leeway than it has already been granted. Greece's creditors slashed interest rates on their loans to well below market rates. The interest payments on many of those loans have been deferred until 2022. In addition, the ECB and national central banks agreed to return the profits they make on Greek bonds to Athens, provided the government sticks to its commitments.

Greece's interest burden equaled about 4% of its economic output in 2014. When adjusting for the profit refunded to Greece and other measures, however, the interest burden was just 2.6%, according to researchers at Brussels-based think tank Bruegel. That compares to 4.7% for Italy and 3.3% for Spain.

Bruegel calculated that Greece could reduce its financing needs by more than EUR30 billion over the next 35 years through a mix of extending maturities and cutting interest rates on some of its loans to zero.

Even if Europe would agree to those measures, it is unclear whether Syriza's supporters would accept any deal that involves more austerity.

While many Syriza voters say they don't expect the party to make good on all of its campaign promises, it would nevertheless be tricky for Syriza's leadership to back away from its core antiausterity platform.

Yet if it doesn't, Greece would likely be forced to default on its debt. Such a scenario would force the ECB to choke off the liquidity it provides Greek banks and the country would likely have to abandon the euro.

German officials have been particularly insistent that Greece stick to the program it has agreed to.

"We believe Greece has accepted terms that are not off the table after the election," German Chancellor Angela Merkel's spokesman, Steffen Seibert, said in Berlin.

A top European Central Bank official said the bank wasn't willing to write off any of the Greek debt it holds. "Mr. Tsipras must pay," ECB executive board member Benoît Coeuré said in an interview with French radio station Europe1. "If he doesn't pay, it's a default and it's a violation of the European rules."

Greece owes around EUR40 billion to France and EUR60 billion to Germany, Mr. Coeuré said. "The debt is owed to taxpayers, not speculators or financial markets. Canceling that debt would be a EUR240 billion gift to Greece."

Laurence Norman, Andrea Thomas, David Román and Inti Landauro contributed to this article.

Write to Matthew Karnitschnig at matthew.karnitschnig@wsj.com, Gabriele Steinhauser at gabriele.steinhauser@wsj.com and Laurence Norman at laurence.norman@wsj.com