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(Adds economic activity data)
MEXICO CITY, June 24 (Reuters) - Mexican annual inflation rose in early June for the first time in five months but stayed within the central bank's tolerance zone, backing bets for steady interest rates ahead.
Inflation for the 12 months through the first half of June rose to 3.71 percent, data showed on Tuesday, just below expectations for a 3.74 percent rise, and well above a seven-month low of 3.44 percent reached in the first half of May.
It was the fastest pace since early March, and the first early month rise since January, after annual inflation reached 3.51 percent in the full month of May.
The annual pace of consumer price gains had been falling back after a spike above the central bank's 4 percent limit early this year due mostly to new taxes on soft drinks and junk food.
Mexico's central bank unexpectedly slashed interest rates to a record low earlier this month, saying a sluggish economy gave it room for a one-off cut to spur growth without fanning inflation pressures.
Growth sank to a 4-year low of 1.1 percent in 2013.
The central bank, which cut its 2014 growth forecast to between 2.3 and 3.3 percent from a range of 3 to 4 percent, could further lower its estimate after first-quarter growth was weaker than expected.
Consumer prices rose 0.08 percent in the first half of June, compared to forecasts for a 0.12 percent rise, as tomato, gasoline and beer prices rose.
The measure had fallen 0.37 percent in early May, due to summer electricity subsidies and a drop in some fresh food prices.
Core consumer prices, which exclude some volatile food and energy prices, picked up 0.12 percent, above expectations for a 0.10 percent rise, and up from the 0.06 percent rise seen in early May.
A separate report showed Mexico's economy grew 1.25 percent in April at a seasonally adjusted pace compared to the prior month, its best showing since November 2012, thanks to a strong services sector.
The figure was well above the upwardly revised 0.61 percent contraction registered in the prior month and exceeded the 0.90 percent expansion expected in a Reuters poll.
Compared to April 2013, economic activity expanded 0.5 percent, compared to forecasts for a 0.20 percent rise and an upwardly revised 3.24 percent increase the prior month. (Reporting by Alexandra Alper; Editing by Andrea Ricci)