"Week by week, we're seeing markets enter corrections as Greece steps closer to the edge"
Euclid Tsakalotos took over as Greek finance minister following the resignation of Yanis Varoufakis.
Europe's Stoxx 600 Index ended the session with a 0.4% decline from the previous close.
Better US data rallies Wall Street.
Eurogroup ministers will discuss the fresh Greek proposal on a teleconference in Brussels as Greece's current aid programme is set to expire.
Greece's Athens Stocks Exchange was closed and will remain shut until at least July 6.
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