Mexico's annual inflation rate cooled in July, posting a record low for a third month in a row, official data showed on Friday, pointing to little pressure on prices from a sharp slump in the peso this year.

The national statistics institute said inflation in the 12 months through July eased to 2.74 percent from 2.87% in June. A poll of analysts by Reuters had forecast a rate of 2.75%.

The annual rate was the lowest on record, according to central bank data going back to 1970, holding below the central bank's 3 percent target for a third month.

Inflation is expected to remain below 3 percent for the rest of the year, but the central bank is still forecast to raise interest rates when U.S. borrowing costs move higher, even though Mexican economic growth is sluggish.

Policymakers are concerned a further tumble in the peso could hit inflation expectations. The peso has lost more than 20 percent against the dollar since the middle of last year and it hit a record low of near 16.50 per dollar in July.

Last week, Mexico boosted its dollar auctions to defend the currency and central bank governor Agustin Carstens warned the bank could raise interest rates at any time, even before the Fed, if the peso needs the support.

Economists think the central bank is unlikely to move before the U.S. Federal Reserve unless the peso weakens much further.

"If this continues, we have a problem, but we don't have a problem with the peso at 16.50, particularly when inflation is running below the target," said Alberto Ramos at Goldman Sachs in New York.

The Mexican data showed that consumer prices rose by 0.15 in July, just below expectations. The core price index, which strips out volatile food and energy prices, climbed 0.17 percent, in line with the poll.

The 12-month core inflation rate came in at 2.31 percent, also in line with forecasts.