PARIS (Reuters) - It is now possible that Greece may end up exiting the euro zone even though this is not what the European Central Bank or other EU institutions want, ECB executive board member Benoit Coeure said on Monday. It was the most direct admission yet by a top ECB policymaker that a "Grexit" could happen after Athens decided to interrupt talks on an aid-for-reforms package and call a referendum for July 5. Greece's bailout expires on June 30 and it has a 1.6 billion-euro ($1.77 billion) payment falling due to the International Monetary Fund at the same time. "A Greek exit from the euro zone, so far a theoretical issue, can unfortunately not be excluded any more," Coeure told the French financial daily Les Echos, adding that this was the consequence of Athens' decision to end the talks. Coeure said that if Greeks vote "Yes" in the referendum for the aid package, he had "no doubt" euro zone authorities will find ways to meet commitments toward Greece. If the "No" vote wins, "it would be very difficult to resume political dialogue," he said. While Greek Prime Minister Alexis Tsipras hopes that his negotiating position would be strengthened by a "No" vote on the lenders' proposal, Coeure warned that euro zone finance ministers had clearly decided that the latest proposal had "reached the limits of what is acceptable." Asked what he would say to convince the Greek people to stay in the euro, the top ECB policymaker gave a stern warning: "If Greece was to leave, austerity would be even worse. It would not benefit anymore from the euro zone solidarity that has given it time to make necessary adjustments." Stunned Greeks faced shuttered banks, long supermarket lines and overwhelming uncertainty on Monday as the breakdown in talks with international lenders plunged their country deep into crisis. Coeure said market reaction nevertheless "remained relatively mild," which he said showed Greece was a unique case faced with a unique situation. But the central bank is monitoring the situation closely and will use all available instruments, or even new ones, if needed, he added. Coeure said the ECB would maintain its support to Greek banks "until further notice" and was reviewing the situation constantly. He said the ECB's decision on Sunday not to raise a cap on emergency funding to Greek banks (ELA) was required by the events of the weekend. It is "a proportionate decision" because it is not "irreversible", he said. The ECB rejected a request by Greece for 6 billion euros of extra emergency funds on Sunday, but is expected to continue limited support for its banks until the referendum, people with knowledge of the matter said earlier on Monday. (Reporting by Ingrid Melander; Editing by Angus MacSwan and Alan Crosby)