European leaders appealed to Greeks to vote “yes” in a referendum on their country’s bailout, warning that the risk of Greece’s exit from the euro was real, as Athens confirmed it wouldn’t be able to make a loan repayment to the International Monetary Fund due on Tuesday.

The Greek government’s decision to call a vote on measures its creditors demand in return for more bailout aid has cast the country into uncharted waters. As of Tuesday, Greece will be cut loose from international rescue loans for the first time in more...