Greece needs to move swiftly to pass a first lender review of economic reforms in coming weeks and to start debt negotiations, Prime Minister Alexis Tsipras said, urging his new ministers to work more and chat less.

The firebrand leftist cemented his position as Greece's dominant political figure national elections in which his Syriza party won 145 of 300 parliamentary seats.

But he faces a tough start to his second term in office, implementing austerity mandated by creditors while seeking debt relief and coping with waves of refugees landing on Greece's shores that have put the country on at the front line of the largest migration flows Europe has seen since the Second World War.

He may also need to work harder than he hoped to maintain what promises to be a volatile coalition between Syriza and the right-wing Independent Greeks party, which won 10 seats.

Independent Greeks lawmaker Dimitris Kammenos resigned as deputy infrastructure and transport minister on Wednesday hours after his appointment due to allegations - which he denied - that he posted anti-Semitic and homophobic comments online.

"This mandate is translated into one word: work," Tsipras told the first meeting of his cabinet.

It features most of the faces from the Tsipras government that held power for seven months until he called snap elections in August, including Euclid Tsakalotos, an Oxford-trained Marxist economist who built up a relationship of trust with lenders in negotiating the bailout agreement.

The charismatic Tsipras also told his 44-member cabinet: "I chose you as ministers to govern, and solve people's problems. Not to be on early morning TV chat shows."

A first review of progress in implementing Greece's third, 86-billion-euro ($96 billion) bailout is due to start in October

If the review goes well it will open the way towards debt relief, a rallying cry for the Greek government, which argues that a mountain of dues accumulated since its first bailout in 2010 is not viable, shackling the country in perpetuity.

"Debt restructuring will reduce investment risks and make our economy once again attractive to investors," Tsipras said.