The Mexican peso was down by 0.8% at 19.0611 per US dollar at 2:19 p.m. ET after being down by as much as 1.0% about a half hour earlier.
"Renewed fears that NAFTA re-negotiation talks may break down, causing the agreement to collapse, have taken a toll on the Mexican peso in recent weeks," Oliver Jones, assistant economist at Capital Economics, said in a note to clients.
The Trump administration came in strong last week for the fourth round of NAFTA re-negotiations, much to the chagrin of Mexico and Canada.
The US presented a number of tough proposals, reportedly including raising the auto rules of origin to 85%, up from the current 62.5%, and adding a sunset clause, which would lead to NAFTA expiring every five years unless all three countries agree to extended it.
One trade official told reporters Saturday "the atmosphere is complicated," and added that his fears about some "pretty harsh, pretty horrible" demands from the US were coming true.
If the US, Canada, and Mexico can't reach a new deal, trade among the three countries could go back to WTO rules, which would see higher "most favored nation" tariffs applied on Mexico's exports to the US, according to Jones.