The U.S. dollar index went up on Tuesday as Turkey's economic turmoil continued to weigh on the euro.

Market anxiety about European banks' exposure to Turkey has hit the euro severely, which plunged to its 13-month lows against the dollar on Tuesday.

The Turkish lira, however, rebounded 6.7 percent against the greenback on Tuesday, after slumping to an all-time low of 7.24 on Monday.

According to U.S. data company FactSet, the lira has dropped more than 40 percent against the dollar so far this year, including almost 25 percent in August alone.

The dollar index, which measures the greenback against six major peers, rose 0.35 percent at 96.738 in late trading.

In late New York trading, the euro was down to 1.1338 dollars from 1.1392 dollars in the previous session, and the British pound decreased to 1.2711 dollars from 1.2751 U.S. dollars in the previous session. The Australian dollar was down to 0.7234 dollar from 0.7260 dollar.

The U.S. dollar bought 111.20 Japanese yen, higher than 110.67 Japanese yen of the previous session. The U.S. dollar increased to 0.9945 Swiss franc from 0.9936 Swiss franc, and it fell to 1.3084 Canadian dollars from 1.3142 Canadian dollars.