The group of 20 major economic powers will recognise the eurozone's efforts to establish a regional banking union at their two-day meeting, a source close to the French presidency has said.

"The final declaration mentions the work being done toward a banking union" and towards "more financial stability", the official said.

The draft final communique of the G20 leaders, meeting in Los Cabos, Mexico mainly on the European economic crisis "mentions that this banking union has been endorsed by all of the members of the eurozone," the source said.

European Union President Herman Van Rompuy and European Commission chief Jose Manuel Barroso said member states were working hard to resolve the crisis, and that establishing a single system for overseeing eurozone banks was a priority.

Meanwhile, the French source said the final G20 declaration would also endorse the position that Greece is and will remain in the eurozone, but also insist that Athens needs to meet its bailout commitments.

The G20 leaders showed clear relief with the results of Greece's elections, in which the centre right New Democratic party came in ahead of the leftist Syriza, which wants to tear up Athens' pledge to impose a harsh austerity program.

Earlier, US President Barack Obama had felt "encouraged" by Europe's plans to move out of its economic crisis after talks today with German Chancellor Angela Merkel, the White House said.