Traders cheered the hints of a tentative deal, after months of drawn out bailout talks between Greece and its international bailout supervisors, propelling the French CAC index to close around 2 percent higher and Greek stocks to end around 3.5 percent higher.
London's FTSE and Germany's DAX both ended around 1.2 percent higher.
Greek Prime Minister Alexis Tspiras said he was "close to an agreement" in a statement and that the deal would be positive for the Greek economy, adding there was "absolutely no danger" to pensions, salaries, banks or deposits in the potential deal.
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On Tuesday, Greece and its Europeans creditors sought to play down fears that Athens would default on a June 5 debt payment to the International Monetary Fund.