The Brazilian real and the Chilean peso initially opened stable but weakened later as key US stock indexes continued last week's slide, turning investors more averse to risk in general.
Investors fear US policymakers will fail to negotiate a timely solution to the so-called "fiscal cliff," a combination of government spending cuts and tax increases that kick in early 2013, possibly plunging the world's largest economy into another recession.
The Brazilian real last traded 0.3 percent weaker at 2.0517 per dollar, after touching a four-month low of 2.0671 per greenback during Friday trading.
"The currency is just tracking international markets. The US bourses opened lower, we have this concern about the US fiscal cliff," said Mauricio Nakahodo, an economic research consultant with Tokyo-Mitsubishi bank in Sao Paulo.
"Besides that, Greece remains a source of trouble," he added.
Greece approved a tough 2013 budget over the weekend, but euro zone finance ministers will not agree to disburse more money to the country at a meeting on Monday because there is not yet consensus on how to make Athens' debts sustainable into the next decade.
Chile's peso fell 0.3 percent to 480.30 per dollar.
In Mexico, however, the peso held steady at 13.1965 per greenback as dollars flew into the country's domestic bond market.
"We're seeing the opposite of what we saw last week. The peso was under a lot of pressure by markets due to the uncertainty in the US, but I think that possibly these levels are attracting foreign investors to purchase bonds," said Rafael Camarena, an analyst with Santander Bank in Mexico City.
"Possibly that is what is moderating the pressures on the peso," he added.