a seven-billion-euro tranche of financial aid from the 28-member bloc and the International Monetary Fund.
Tsipras, who has vowed to reverse many of the belt-tightening measures that Greece´s creditors insisted on, must decide whether to prolong the deadline.
Syriza hopes that its strong mandate -- it holds 149 seats in the 300-member parliament -- will help it to force through a new deal with Brussels.
"If there is a willingness on both sides, a solution will be found," Dragassakis told AFP in an interview just days before Sunday´s election.
Syriza claims the stringent conditions attached to the bailout granted in 2010 have caused a "humanitarian catastrophe" in Greece. It wants to release an immediate 1.2 billion euro plan to increase the minimum wage and pensions.
The first foreign dignitary to visit Greece since Syriza became the first anti-austerity party to take power in Greece will be the social democrat head of the European Parliament, Martin Schulz, on Thursday.
Having fallen two seats short of an absolute majority, Syriza swiftly forged a governing coalition with the small right-wing Independent Greeks (ANEL) party.
Analysts have described the coalition as "unnatural" and potentially short-lived, saying that that ANEL are unpredictable, while the two parties differ starkly on immigration policy.
However, the two parties share a common opposition to the EU-IMF bailout.
Fears that Greece could be forced out of the eurozone if it defaults on its debt repayments saw the euro briefly hit an 11-year low against the dollar on Monday, but it improved in Tuesday trade. The IMF extended an olive branch to the new Greek government, saying it was prepared to continue its financial support to the country.
"We stand ready to continue supporting Greece, and look forward to discussions with the new government," IMF managing director Christine Lagarde said in a statement.
Greece´s economy is set to emerge from recession after shrinking by a quarter in five years and leaving one in four people out of work.
Many Greeks say that even if Tsipras can deliver on a fraction of what he has promised, their lives will improve.
After the new prime minister was sworn in on Monday, Eleni, 41, said: "We are just asking to be able to live like any other European citizen.
"At the moment if you go to a state-run hospital in Greece, you feel as if you are in a warzone.
"Repaying the debt does not justify subjecting people to such suffering," she said. Sunday´s poll was Greece´s fourth in five turbulent years, including back-to-back votes in 2012.
Tsipras stands alone as Europe´s first anti-austerity leader for the moment, but Syriza´s victory could inspire other anti-austerity parties, including Spain´s Podemos, which has topped several opinion polls and is aiming for an absolute majority in the Spanish election in November.