Inflation in the 12 months through mid-June was 2.55 percent , the national statistics institute said. That was below a forecast 2.63 percent in a Reuters poll and the 2.6 percent rate at the end of May.
But core inflation crept up to nearly 3 percent in early June, and policymakers are concerned that a prolonged peso slump could hit inflation.
The peso is down nearly 6 percent against the greenback this year but has recovered somewhat this week.
Mexico's central bank may raise interest rates at its next meeting on June 30, but bets in the interest rate swap market are divided .
Consumer prices rose 0.02 percent in the first half of June , compared with expectations of 0.11 percent.
The closely watched core price index, which strips out some volatile food and energy prices, climbed 0.16 percent in early June, compared with forecasts for a 0.14 percent increase.
The 12-month core inflation rate rose to 2.98 percent , slightly above the poll's expectations of 2.96 percent.