MSCI's index of Latin America stocks rose 0.5 percent, while the regional currency index erased earlier losses to trade flat.
The real gained half a percent while Mexico's peso was up 0.6 percent, coming off the more than one-and-a-half-month lows hit on Wednesday.
Gabriela Siller, director of financial and economic analysis at Banco BASE, said a return of risk appetite was a factor in the appreciation of the peso and real.
Brazil is headed for a presidential election run-off on Sunday. Polls show far-right candidate Jair Bolsonaro, the favorite of investors, likely to defeat leftist Fernando Haddad.
"There is a lot of optimism in Brazilian assets, overall," said Mauricio Oreng, senior Brazil strategist with Rabobank.
"There could be some downside (for the real), but that would depend on the policies of the new administration ... if Bolsonaro wins. Given the signs so far, the markets are constructive."
Stocks in Brazil, Latin America's largest economy, were up 1 percent on Thursday, exceeding the 0.4 percent gain seen in Mexico's equity benchmark.
Banco BASE's Siller, however, cautioned that the greatest risks to the peso at the moment relate to uncertainty about public policies and the way in which the country's next government could make decisions.
The most immediate test for the incoming administration is what to do about an airport in Mexico City that is under construction. Its fate depends partly on the result of a public consultation, called by President-elect Andres Manuel Lopez Obrador (AMLO), that runs through Sunday.
Obrador believes the project will come in over budget and has been tainted by corruption, and has called for the consultation to help decide if it should be finished or an existing military base should be updated.
In broader Latin America, Argentina's peso gained about 0.4 percent, while Colombia's peso recovered from initial losses which saw it trade at its weakest levels since November 2016.
Colombian stocks were 1.9 percent higher, on track for their best session in about one and a half months.