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(Recasts with annual rate, adds contraction in services sector)
MEXICO CITY, Sept 24 (Reuters) - Mexico's annual inflation rate cooled in early September to a record low while the economy grew less than expected in July on a drop in services output, suggesting policymakers could hold interest rates steady despite a steep slide in the peso.
Inflation in the 12 months through mid-September cooled to 2.53 percent from 2.64 percent in the first half of August, the national statistics institute said on Thursday.
The rate was the lowest reading for the first half of a month since at least 1989, according to data on the institute's website. A poll of analysts by Reuters had forecast the rate would ease to 2.48 percent.
A separate report from the institute showed that the economy grew 0.1 percent in July compared with June, below expectations for a 0.4 percent increase, as the services sector shrank by 0.2 percent in its biggest month-on-month drop since last December.
Inflation is expected to remain below 3 percent for the rest of the year as sluggish growth contains price pressures, but Mexican policymakers said on Monday they are prepared to raise rates if the peso's losses hit consumer prices.
But so far there has been little impact on prices from the peso, which hit a fresh record low earlier on Thursday.
The central bank's benchmark interest rate is at an all-time low of 3 percent.
However, Mexico's central bank is still forecast to raise interest rates in December according to a Reuters poll.
The Mexican data showed that consumer prices rose by 0.32 percent in the first half of September. The analysts' poll had forecast a 0.27 percent increase.
The core price index, which strips out some volatile food and energy prices, climbed 0.27 percent in early September, compared with expectations for 0.26 percent.
The 12-month core inflation rate came in at 2.34 percent, underscoring the so-far limited impact of peso weakness on goods and services. A rate of 2.33 percent had been forecast. (Reporting by Michael O'Boyle Editing by W Simon)