ATHENS (Reuters) - German Vice-Chancellor Sigmar Gabriel said on Thursday Britain's departure from the European Union should be swift.

"The exit of Great Britain must be done at a fast pace," he was quoted as saying in an officially translated transcript of remarks to Greek President Prokopis Pavlopoulos.

"If this drags on it will not be good neither for Britain or Europe. Both must know how the day after will shape up," he added.

"There is no doubt, Europe won't fall apart because the United Kingdom is leaving."

Britain's younger voters, who mostly favored remaining in the EU, were "wiser and smarter" than its leadership, said Gabriel, making a two-day visit to troubled euro zone member state Greece.

But he added that last week's overall referendum vote to leave the bloc was "a legal act which we must fully respect".

Gabriel earlier this week ruled out the possibility of offering Britain something short of full EU membership.

In comments to Greek Prime Minister Alexis Tsipras during a separate meeting on Thursday, Gabriel said people were more inclined to swing to the political right and against the EU "when their lives are getting worse".

"We saw it (in the British referendum) that poor people voted for 'out'. We saw it years ago in the Irish referendum where workers voted against Europe. We need a new approach in Europe," he said.

(Reporting by George Georgiopoulos; writing by Michele Kambas; editing by Andrew Roche)