(Adds economic activity indicator, paragraphs 10-12)
MEXICO CITY, July 24 (Reuters) - Mexican annual inflation rose in early July to touch the central bank's tolerance ceiling, surging to a five-month high as tourism packages, air transport and gasoline prices rose.
Inflation for the 12 months through the first half of July rose to 4.0 percent, national statistics institute data showed on Thursday, above expectations for a 3.95 percent rise and the 3.71 percent rate reached in the first half of June.
Inflation has been rising over the last two months but the central bank, which targets inflation of 3 percent with a 1 percentage point tolerance band, expects inflation to fall back to near 3 percent by the start of next year.
Mexico's central bank cut its benchmark interest rate to a record low of 3 percent in June after weak growth in the first quarter. It held the rate steady in July, noting signs of a stronger economy while still pointing to weak domestic demand.
Deputy central bank governor Manuel Sanchez told Reuters on Monday that the economy likely picked up in the second quarter, adding growth could be stronger in the second half of the year.
Economic expansion sank to a 4-year low of 1.1 percent in 2013.
Consumer prices rose 0.2 percent in the first half of July, compared to forecasts for a 0.15 percent rise, and the 0.08 rate in early June.
Core consumer prices, which exclude some volatile food and energy prices, reached 0.14 percent, above expectations for a 0.11 percent rise, and the 0.12 percent rise seen in early June.
A separate statistics institute report showed Mexico's economy shrank 0.12 percent in May at a seasonally adjusted pace compared with the preceding month, as activity in the services sector sank.
That figure contrasted with a 1.13 percent expansion in April versus March, revised down from an initially reported 1.25 percent expansion.
Compared with May 2013, economic activity expanded 1.41 percent, above the 0.49 percent pace reached the prior month. (Reporting by Alexandra Alper Editing by W Simon)