Mexican inflation accelerated to a 2-1/2-year high in September as prices of fresh food continued to rise although analysts expect no immediate reaction from the central bank.

Annual inflation rose to 4.77 percent last month, up from 4.57 percent in August but just below the 4.78 percent expected in a Reuters poll, national statistics agency data showed on Tuesday.

It was the highest rate since March 2010 and puts inflation even further above the central bank's 4 percent tolerance limit, which it has now overshot for four months in a row.

Still, Banco de Mexico Governor Agustin Carstens has said it is important not to move interest rates from their current 4.5 percent level prematurely, as the central bank is watching for signs that price pressures are spreading through the economy.

"I think they are going to ride this high inflation for a while and hope that they get some relief from agricultural prices (later)," BNP Paribas economist Nader Nazmi said.

Policymakers have said they expect the jump in prices to be transitory and the market is betting on stable interest rates through next year.

The latest increase in consumer prices was driven by a 14 percent annual rise in egg prices, following an avian flu outbreak this year in western Mexico, with overall agricultural prices up 16 percent, the statistics agency said.

Consumer prices rose 0.44 percent in September from August compared with an expected 0.45 percent rate and a 0.30 percent rise in August.

Although the rate of increase in core prices eased, Nazmi said this was due to one-off factors such as lower electricity and telephone line prices and was not necessarily a broader signal on domestic price pressures.

"Some of the views that have been expressed in the past about inflation falling to below the central bank's comfort zone by the end of the year appear overly optimistic -- we don't really see price pressure relief that would bring inflation down," he said.

The core price index, which strips out some volatile food and energy prices, rose 0.18 percent compared with an expected 0.20 percent increase and a 0.22 percent rise in August, and annual core inflation eased to 3.61 percent.

Annual inflation in services, a key gauge of home-grown price pressures, fell to its lowest since February and non-food core goods inflation, the most sensitive to currency fluctuations, eased to 3.96 percent, the first deceleration in almost a year.

Carstens said a recent rise in the peso -- which has rebounded more than 13 percent against the dollar after hitting a three-year low in early June -- would help dampen inflation going forward, but peso moves normally take several months to feed into the price index.

Analysts recently raised their forecasts for inflation this year to 4.15 percent, increasing their estimates in a central bank poll issued last week for the fourth month in a row.

(Editing by Andrea Ricci)