On Monday, the dollar stopped growing against the basket of major currencies, even after data showed that the volume of pending home sales in the US rose to the highest level since 2006, while the concerns about difficult situation in Greece slightly eased.
The US National Association of Realtors reported that its volume of outstanding transactions for the sale of housing increased by 0.9% last month, below expectations for a gain of 1.2%.
The growth rate in April was 2.7%, which was revised up from the previously forecast of 3.4%.
The USD index, showing the relationship of the dollar to the basket of major currencies, was kept unchanged at 95.60, falling from session highs of 96.60.
The EUR/USD fell 0.13% to 1.1149 after falling to 1.0955, the low earlier in the session, while EUR/CHF fell 0.73% to 1.0355.
The euro received some support after SNB Chairman, Thomas Jordan, said on Monday that the central bank intervened in currency markets "in order to stabilize markets" which plunged into chaos after Greece announced the termination of banking work.
The Greek government has decided to suspend the functioning of banks and the central bank began to control the movement of capital, as the banking system is close to collapse due to a significant acceleration of deposit outflows at the weekend.
Earlier, the European Central Bank said it would continue to assist with emergency liquidity to Greek banks; however, the limit of the funding will be at the current level.
On Saturday, Greece broke off negotiations with the creditors, and Prime Minister Alexis Tsipras announced a referendum on July 5, on proposed conditions of creditors to continue bailout program.
European finance ministers refused to renew financial assistance to Greece, in spite of the request of the Greek authorities to extend the program until the results of the referendum.
Athens on Tuesday will have to pay 1.6 billion euro to the International Monetary Fund, but without the bailout package is unlikely that payment will take place.
The pound also went down; the pair GBP/USD fell 0.15% to 1.5726.
Earlier data showed that net lending to individuals increased in the UK last month with 3.1 billion pounds, lower than the previously projected 3.3 billion pounds, but more than 2.9 billion pounds in April.
The dollar fell against the yen and Swiss franc; USD/JPY pair fell 0.80% to 122.85 and the pair USD/CHF fell 0.43% to 0.9288.
The dollars of Australia and New Zealand showed a decline; AUD/USD fell 0.19% to 0.7644 and the pair NZD/USD fell 0.42% to five-year low of 0.6813.
Meanwhile, the pair USD/CAD rose 0.67% to get traded at 1.2404.