MEXICO CITY (Reuters) - Mexico's annual inflation rate rose faster than expected in early July, driven up by higher gasoline prices, but it was still below the central bank's target.

Inflation in the 12 months through mid-July rose to 2.72 percent <MXCPHI=ECI>, the national statistics institute said on Friday. That was above a forecast of 2.66 percent in a Reuters poll and the 2.55 percent rate in early June.

Mexico's central bank targets a rate of 3 percent. Despite relatively tame inflation and weak growth, a steep slump in the peso <MXN=> pushed policymakers to raise interest rates by more than expected in late June.

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. Policymakers are concerned that the prolonged slump in the peso could hit inflation.

On a monthly basis, consumer prices rose 0.28 percent in the first half of July <MXCPIF=ECI>, above expectations of 0.22 percent, with higher gasoline prices having the biggest effect.

The core price index climbed 0.11 percent in early July, lower than forecasts for a 0.15 percent increase, helped by a drop in mobile phone costs.

(Reporting by Michael O'Boyle; Editing by Lisa Von Ahn)