Renewed worries that Trump would scrap NAFTA had weighed on the peso last week. The talks between the United States, Mexico and Canada are edging closer to the start of campaigning for Mexico's July 1 presidential election, making a breakthrough more unlikely.

However, market participants cited a media report by Axios news site on Sunday that said Trump may be shying away from terminating NAFTA, fearing it would disrupt a US stock market rally and harm farmers and agricultural communities, part of his core constituency.

Trump has said he wants the treaty renegotiated to better favor US interests, and that he will scrap NAFTA if this cannot be achieved. Mexico sells around four-fifths of its exports to the United States so it is particularly vulnerable to increased US protectionism.

The peso strengthened 1.3 percent, by far the biggest gainer in Latin America. Low trading volumes on Monday due to the US Martin Luther King Day holiday helped to accentuate currency moves.

In a client note, Continuum Economics said that strength in the peso should continue in the first quarter ahead of this year's elections.

"At least for a quarter, investors will be gaining a good carry in one of the most liquid currencies in emerging markets. After one quarter, we may see a return to defensive positions as the market dives into Mexican presidential elections," the note said.

Other currencies in the region, such as the Brazilian real and the Chilean peso, also firmed on the heels of global US dollar weakness.

The dollar has dropped as markets grow increasingly confident that central banks will wind down their monetary stimulus. Measured against a basket of currencies, the dollar was down 0.2 percent on Monday, its lowest since early 2015.