MEXICO CITY (Reuters) - Mexico's annual inflation picked up in May but remained below the central bank's 3 percent target, giving policymakers room to keep interest rates on hold amid concerns about a weak currency.

Inflation in the 12 months through May rose to 2.60 percent, the national statistics agency said on Thursday. That compared with a forecast of 2.58 percent in a Reuters poll and April's 2.54 percent annual rate.

After falling to a record low in May 2015, inflation in Latin America's No. 2 economy is posting the longest period on record below the central bank's 3 percent target.

Still, Mexican policymakers unexpectedly raised interest rates in February to support the peso, which has tumbled since late 2014 to record lows during a slump in world oil prices and worries about global growth.

Last month, central bank Governor Agustin Carstens suggested policymakers would be reluctant to make another unexpected move even after the peso fell by the most in May in four years.

Taking pressure off the central bank, the peso <MXN=> has bounced back in June, after weak jobs data in the United States dampened expectations that the U.S. Federal Reserve will raise borrowing costs this month.

The new data showed consumer prices <MXINFL=ECI> fell 0.45 percent in May, in line with estimates in the Reuters poll and the second consecutive monthly drop, on summer electricity cost subsidies and lower tomato prices.

The core index, which strips out some volatile food and energy prices, rose 0.21 percent during the month <MXCPIX=ECI>, just below the 0.22 percent estimate seen in the poll.

The 12-month core inflation rate rose to 2.93 percent <MXCCPI=ECI>, its highest since December 2014, from 2.83 percent in April. The figure was in line with forecasts.

(Reporting by Michael O'Boyle; Editing by Lisa Von Ahn)