The U.S. dollar dropped against its most major counterparts in the early European session on Wednesday, after the U.S. President Donald Trump threatened to shutdown federal government unless the Congress funds money to build a border wall with Mexico and also hinted at the possible termination of the NAFTA (North American Free Trade Agreement) deal.

Trump said in Arizona on Tuesday that he would be willing to let the government shut down without appropriations for a border wall. He also expressed doubts whether the U.S. can reach a deal with Canada and Mexico over the North American Free Trade Agreement, adding that the U.S. government will "probably" terminate the trade agreement. Trump's speech weighed on the market on Wednesday, pushing safe-haven currencies higher.

The dollar index, which measures the greenback against six major peers, was down 0.41 precent at 93.160 in late trading.

In late New York trading, the euro climbed to 1.1810 U.S. dollars from 1.1751 U.S. dollars, and the British pound declined to 1.2800 U.S. dollars from 1.2826 U.S. dollars. The Australian dollar decreased to 0.7900 U.S. dollar from 0.7906 U.S. dollar.

The U.S. dollar bought 109.03 Japanese yen, lower than 109.52 yen of the previous session. The U.S. dollar fell to 0.9655 Swiss franc from 0.9684 Swiss franc, and it edged down to 1.2553 Canadian dollars from 1.2562 Canadian dollars.