* Central bank leaves rates at 4.5 percent * Central bank warns may hike rates in future * Inflation jumps to more than two-year high By Krista Hughes and Simon Gardner MEXICO CITY, Sept 7 (Reuters) - Mexico's central bank left interest rates on hold on Friday but signaled it may tighten monetary policy in the future after inflation jumped to its highest in almost 2-1/2-years on the back of high food prices. The Banco de Mexico kept benchmark credit costs at 4.5 percent, as expected, but said it was watching inflation closely to make sure that high food prices, a weak peso and loose policy in advanced economies did not pressure local prices. "In the future, the board will remain alert to the evolution of all determinants of inflation, given that their behavior could make it advisable to adjust the reference rate upwards," the central bank said in a statement. After its last meeting in July, the central bank had given an equal chance to cutting rates as it did to raising them and the change in tone prompted some investors to price in a rate hike, but only in 2014. The peso, which was buoyed on Friday by the possibility of the Federal Reserve pumping more money into the U.S. economy, was little moved by the central bank's statement. Economists were unconvinced that the bank was seriously considering a rate increase, and said the statement reflected differences of opinion on the five-member board. "What they are saying is looking at all this they see it's more probable that they're going to hike than cut," said Alberto Ramos from Goldman Sachs. "However when you look at the balance of risks that could lead to a hike, I think it's not there." Data earlier on Friday showed annual inflation through the end of August accelerated to 4.57 percent, the fastest rate since March 2010 and well above the central bank's 4 percent ceiling. The Mexican central bank, the Banco de Mexico, has held benchmark rates at 4.5 percent since mid-2009 as the economy recovered from a deep recession, and a hike would put it in sharp contrast to counterparts in Colombia and Brazil, which has slashed official interest rates to record lows and may have one more cut to go. However, David Rees of Capital Economics said that headwinds for the Mexican economy would likely increase and that there was little chance of the central bank raising interest rates. "Instead, we think that rates are likely to remain on hold for the foreseeable future, with a strong possibility of cuts next year as the economy slows," he wrote in a research note. Mexico's fortunes are closely tied to the United States, and positive recent data north of the border fanned hopes Mexico can withstand shakiness in the global economy, which has been hit by worries about Europe. So far, resilient domestic demand has not fanned price pressures, although inflation has now overshot 4 percent for three straight months after bad weather and an outbreak of avian flu drove up food prices. INFLATION JUMP Policymakers said risks to growth had continued to worsen due to global economic woes. They expected inflation to remain above 4 percent in coming months, but said risks were easing in the medium term. The headline annual inflation rate exceeded analysts' expectations for an increase to 4.52 percent. Consumer prices rose 0.30 percent in August compared with a Reuters poll estimate of 0.27 percent, but eased from July. Egg prices rose 11 per cent in the month and annual inflation in agricultural prices overall accelerated slightly to 11.76 percent. The central bank said it expected the impact from food prices to be transitory. Core inflation, which strips out some volatile food and energy prices, rose 0.22 percent, in line with expectations and also lower than July. On an annual basis, core inflation was 3.70 percent - suggesting home-grown price pressures are relatively contained. Still, the central bank said the weak peso was pushing up inflation by making some imported goods more expensive. Non-food core goods inflation, the most sensitive to currency fluctuations, accelerated to 4.01 percent in the 12 months through August, from 3.6 percent in July. The peso has recovered about 10 percent from a three-year low hit in early June to trade at just under 13 per dollar on Friday. Having earlier traded as low as 12.9413 against the dollar, the peso was back at around 12.99 by 1515 GMT. Inflation last exceeded the central bank's tolerance limit for three straight months in late 2010. The central bank aims for inflation of 3 percent, plus or minus 1 percentage point. Still, new measures designed to combat the spike, such as temporarily dropping tariffs on imported eggs, should begin to slow the inflation rate soon, analysts said.