The peso sank to a three-year low at the start of June on concerns Europe's debt troubles could spark another global financial crisis.
The currency surged back to a one-month high on Tuesday, helped by bets the US Federal Reserve could deliver more monetary stimulus.
Mexican Central Bank Governor Agustin Carstens said it was difficult to see a clear end to the volatility.
"I hope it is soon, but we have to be prepared to live with turbulence for some time. It could be a question of more than a year," Carstens told broadcaster Televisa in an interview.
"We are going to have volatility in the markets," he said, adding that "the strong fundamentals of the Mexican economy will maintain stability in the medium and long term."
On Monday, Carstens said the volatility could last for months.
The central banker spoke on the sidelines of the Group of 20 summit of the world's top economies in the resort of Los Cabos, where anxious world leaders are pressing Europe to take bolder steps to stem its debt crisis.
Carstens noted the peso was trading around levels where it ended 2011. The currency had been one of the top gainers among emerging markets during the first quarter, but then fell the most of any Latin American currencies in May.
"This year we have not had a net depreciation. This is a adequate level, given the circumstances, but (the peso) has the potential to strengthen," Carstens said.
Mexico's peso is one of the most easily tradable emerging market currencies, making it a target for speculators despite the country's slim, direct links to Europe's economies.
Brazil has aggressively protected its currency, but Mexico has held back from ad-hoc interventions and relies on a dollar auction program that has only been triggered twice this year.
Earlier this month, Mexico's central bank held borrowing costs steady and seemed to rule out an interest rate cut any time soon due to concern that a weak peso could fan inflation.