"We face the obligation to quickly implement what has been agreed," Tsipras told his new government's inaugural cabinet meeting.
In the closing days of Tsipras' last administration, Athens signed up to more tax hikes and public spending cuts in return for a three-year, 86-billion-euro ($96-billion) EU bailout.
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The U-turn split Tsipras' ruling Syriza party and forced him to step down, but he comfortably won re-election on Sunday with a pledge to mitigate the impact of the bailout.
"We are aware of the difficult points of the deal... We know how to find the right antidote where there are side effects," Tsipras said today.
In a positive signal to creditors, Tsipras brought back the team that brokered the bailout -- with Euclid Tsakalotos returning as finance minister and top negotiator George Chouliarakis appointed junior finance minister.
In the coming weeks, the government must present an overhaul to make the country's underfunded pension system viable and introduce sweeping tax hikes.
Greece's new parliament, expected to convene on October 1, will also have to revise the 2015 budget, taking into account the reforms, including taxes on farmers' income that are set to double by 2017.
The government must also finalise a procedure to recapitalise Greek banks by December, before new EU-wide bank rescue regulations that could affect depositors come into play in 2016.
And Tsakalotos will have to move quickly to remove capital controls imposed in June to avert a deposit run.
In late October, the lenders will conduct an audit to determine whether Athens is abiding by the reform programme. The release of a three-billion-euro ($3.3-billion) tranche of aid depends on its findings.
"It is critical not to lose an inch from the ground gained in the deal," Tsipras said, telling ministers they had "no time" to lose, and urging them to stay off television.
"I call you to immedately halt your constant television apperances... I selected you as ministers to solve problems, not to staff talk show panels," the premier said.
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