U.S. dollar retreated on Monday against the British Pound ahead of Tuesday's Brexit vote.

The pound touched two-month high on Monday against the dollar after a report showed that a a pro-Brexit faction of lawmakers could support UK Prime Minister Theresa May's Brexit deal in parliament.

The dollar index, which measures the greenback against six major peers, decreased 0.06 percent at 95.6124 in late trading.

In late New York trading, the euro was unchanged at close to 1.1465 dollars from 1.1465 dollars in the previous session, and the British pound rose to 1.2865 dollars from 1.2845 U.S. dollars in the previous session. The Australian dollar was down to 0.7198 dollar from 0.7206 dollar.

The U.S. dollar bought 108.20 Japanese yen, lower than 108.48 Japanese yen of the previous session. The U.S. dollar fell to 0.9813 Swiss franc from 0.9844 Swiss franc, and it was down to 1.3267 Canadian dollars from 1.3271 Canadian dollars.