The annual reading of the core price index MXCPIC=ECI, which strips out some volatile food and energy prices, ticked up to 2.99 percent in early July.
Inflation in the 12 months through May rose to 2.60 percent, the national statistics agency said on Thursday.
The central bank expects inflation to rise slightly above its 3 percent target during 2016, but fall back toward the target by the end of the year.
The majority of the board members are worried about the risk that global volatility could spark a "disorderly" drop in the peso that could have a bigger impact on inflation.
Inflation in the 12 months through April cooled to 2.54 percent, the national statistics agency said on Monday.
Mexico's annual consumer price inflation rate stood at 2.60 percent in the 12 months through March.
Inflation in the 12 months through March cooled to 2.60 percent, the national statistics agency said on Thursday.
The central bank expects inflation to rise slightly above its 3 percent target during 2016, but fall back toward the target by the end of the year.
Inflation in the 12 months through February rose 2.87 percent, the national statistics agency said.
These inflation rates have taken completely divergent paths even as Mexico’s peso, just like Brazil’s real, sets record lows one session after another against the U.S. dollar.