The euro weakened against the other major currencies in the early European session on Tuesday, as sentiment dampened ahead of the emergency Eurozone leaders'summit on Greece crisis, scheduled for later today. The outcome of the Greek referendum is very regrettable for the future of Greece as it made discussions with its creditors more difficult, Eurogroup chief Jeroen Dijsselbloem told reporters on Monday. However, he said that keeping Greece in the euro zone is still their objective.

Greece prepares to present new proposals to its international creditors, as leaders of France and Germany have asked Greece to come up with serious proposals at the Eurozone summit in order to restart financial aid talks. Separately, International Monetary Fund chief Christine Lagarde said that the global lender stands ready to assist Greece if requested to do so.

Meanwhile, contagion fears may ease a little bit after the Governing Council of the European Central Bank maintained its stance on emergency funding to Greek banks. However, the ECB said it would raise the haircuts on Greek bank collateral, most of which is made of Greek government bonds. The move could make it difficult for the country's banks to access ELA funds in future. Greek banks will remain shut until at least Thursday, with limits on daily withdrawals unchanged, officials said.

The Grexit fear raised after Greek voters rejected austerity measures proposed by the country's international creditors in a weekend referendum.

Meanwhile, the European share market also traded lower. The U.K.'s FTSE 100 index is currently down 0.28 percent or 18.47 points at 6,517, France's CAC 40 index is down 0.30 percent or 14.35 points at 4,697 and Germany's DAX is down 0.26 percent or 27.32 points at 10,862.

In other economic news, data from Destatis showed that Germany's industrial production remained unchanged in May from the prior month. Production was forecast to rise 0.1 percent after expanding 0.6 percent in April, which was revised down from 0.9 percent. In the early European session, the euro slid to an 8-day low of 1.0957 against the U.S. dollar, from an early high of 1.1057. On the downside, 1.07 is seen as the next support level for the euro.

The euro fell to 0.7059 against the pound, 134.80 against the yen and 1.0396 against the Swiss franc, from early highs of 0.7089, 135.66 and 1.0427, respectively. If the euro extends its downtrend, it is likely to find support around 0.68 against the pound, 130.00 against the yen and 1.02 against the franc.

Against the Canadian dollar, the euro edged down to 1.3935 from an early high of 1.3988. The euro may test support near the 1.34 region.

Looking ahead, Canada and U.S. trade balance, both for May and U.K. NIESR GDP estimate for June are scheduled to be released in the New York session.

Eurozone finance ministers are due to meet to discuss Greece later in the day.

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