After re-election win, Syriza faces challenges of implementing austerity measures and Europe’s refugee crisis.

Alexis Tsipras is expected to be sworn in as Greece’s prime minister on Monday after his left-wing Syriza party decisively beat its conservative rivals in Sunday’s national elections. But there is no honeymoon period for the 41-year-old leader, who must quickly address a double challenge: the implementation of politically explosive pension cuts and other austerity measures under Greece’s bailout plan, and a refugee crisis that Greece’s parties have mostly avoided until now. With 99.95% of the vote counted Monday, Syriza had won the 35.5% of the vote, followed by 28.1% for conservatives New Democracy. The fascist movement Golden Dawn came in third place with 7%, closely by socialists Pasok on 6.3%. Syriza said Sunday it would renew its governing coalition with the right-wing nationalist Independent Greeks, who won 3.7% of the votes cast. The announcement means Syriza and Independent Greeks will have a narrow majority of 155 in Greece’s 300-seat parliament. The two parties governed Greece from January to August, when Mr. Tsipras resigned and triggered early elections in a bid to renew his majority. Syriza split when some lawmakers rebelled against Mr. Tsipras’ decision to sign an austerity-heavy bailout deal with Europe.

As Mr. Tsipras moved quickly Monday to form his new government, Syriza officials said the next Greek finance minister would almost certainly be Euclid Tsakalotos, who held the post in July and August.

Mr. Tsipras is expected to be sworn in as prime minister later Monday, while his cabinet will be sworn in on Tuesday. European Union officials welcomed Sunday’s election result and urged the new government to stick to the economic overhaul set forth in the bailout agreement.

Analysts say Mr. Tsipras’s second-term coalition may be more stable, with fewer potential rebels because of the departure of the hard-line anti-bailout faction, which didn’t win enough votes Sunday to enter parliament. Mr. Tsipras now has a mandate to implement tough fiscal retrenchment, whereas in January he was elected to overthrow austerity. Beyond that, however, it is mostly uphill for Mr. Tsipras. “The current government will need to both push through deep reforms and run the country at a time when liquidity has evaporated, the migrant issue has become explosive and when big decisions are still ahead,” said Michael Jacobides, associate professor of strategy and entrepreneurship at the London Business School.

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