The Mexican peso gained about 1.5 percent on the day to 19.587 to the dollar MXN=D2, after rising to 19.575 at one point.
"Overall, there seems to be some adjustment of positions that had been betting on Trump risk," said a trader for a Japanese bank.
There seems to be some profit-taking of long dollar positions taken against the Mexican peso, he said.
According to Reuters, the peso has hit record lows in recent days on concerns a Trump victory would threaten Mexico's exports to the United States, its single biggest market.
The safe haven yen retreated from a one-month high set against the dollar earlier on Tuesday.
Against the yen, the dollar was last trading at 100.72 yen JPY=, up 0.4 percent on the day.
The greenback had slipped to as low as 100.085 yen earlier on Tuesday, its lowest level since late August, as caution gripped the market ahead of the U.S. presidential debate.
While both Clinton and Trump are seen favoring a weaker dollar, some fear a Trump victory could expose the U.S. economy to more acute negative shocks with worse consequences for the U.S. dollar.