Greek prime minister Alexis Tsipras is confident that Athens can reach a debt relief deal without leaving the European Union.

Tsipras met with European leaders on Wednesday for the first time since his Syriza party won elections last month.

"I'm very optimistic that we will try to do our best in order to find a common, viable and mutually acceptable solution for our common future," he said after the meeting.

"Our goal is to respect the people's sovereignty in Greece and the clear mandate of our people. At the same time we respect the rules of the European Union. We want to recorrect this framework, not to smash this framework and we believe that in this framework we could find a common viable solution."

Meanwhile Greek finance minister Yanis Varoufakis also sounded a positive note after he met with the president of the European Central Bank.

Varoufakis said he had "fruitful" talks with Mario Draghi after the pair met at the bank's HQ in Frankfurt.

The Greek minister told reporters that he believes that talks would progress quickly and that a resolution is not far-off.

"The ECB is the central bank of Greece... The ECB will do whatever it takes to support the member states in the euro zone," he said.

"I have no doubt that we can conclude our discussions with our European partners, as well as with the IMF and the ECB, in a very short space of time so that we can kick-start the Greek economy."

Varoufakis is due to meet with German finance minister Wolfgang Schauble. Berlin is expected to play a long game with Athens over its debt conditions, waiting for signs of economic recovery before it eases austerity measures on Greece.