"I think we have to take a look at seriously whether or not the UK is allowed to trade. Because you know, right now, if you look at the deal, they may not be able to trade with us," Trump said Monday on the White House's South Lawn.
In response, May on Tuesday defended her Brexit plan, saying that the UK "will be able to do trade deals with countries around the rest of the world."
"As regards the United States, we have already been talking to them about the sorts of agreements that we could have in the future," she said.
The dollar also extended gains after Federal Reserve Vice Chairman Richard Clarida said on Tuesday that the central bank would further back interest rate hikes in a speech delivered to bankers in New York.
"A monetary policy strategy must find a way to combine incoming data and a model of the economy with a healthy dose of judgment and humility to formulate and then communicate a path for the policy rate most consistent with our policy objectives," he said.
In late New York trading, the euro fell to 1.1295 dollars from 1.1329 dollars in the previous session, and the British pound was down to 1.2733 dollars from 1.2811 U.S. dollars in the previous session. The Australian dollar was down to 0.7223 dollar from 0.7228 dollar.
The U.S. dollar bought 113.78 Japanese yen, higher than 113.64 Japanese yen of the previous session. The U.S. dollar decreased to 0.9986 Swiss franc from 0.9991 Swiss franc, and it increased to 1.3299 Canadian dollars from 1.3241 Canadian dollars.