(Adds details, central bank quote, background)

CARACAS, Sept 9 (Reuters) - Venezuela's annualized inflation rate reached 63.4 percent in August, with consumer prices rising by 3.9 percent that month, the central bank said, reaching a fresh six-year high as President Nicolas Maduro wrestles to control spiraling prices.

The central bank, which had not published monthly inflation since May's data, simultaneously released statistics for June, July and August on Tuesday evening.

Critics criticized the delays as a means to hide poor economic data, including the region's highest inflation rate.

Annualized inflation reached 62.0 percent in July, lower than June's 62.2 percent rate. Monthly inflation was 4.1 percent in July, also lower than June's 4.4 percent.

"In summary, month-to-month inflation eased in August for the third straight month," the bank said in its statement. "That's the lowest figure since the month of March."

Opposition-leaning website La Patilla said earlier this week that the bank had changed its methodology to improve the inflation data.

The central bank did not mention a methodological change in its statement. Calls to the bank went unanswered.

Maduro's government has said the bank was preparing to tweak its methodology, but it did not say when a potential change would be implemented.

He has blamed the inflation spiral on months of violent opposition protests at the start of the year. Those protests often blocked roads, forced stores to close early and hindered delivery of merchandise.

Most economists blame spiraling inflation on a torrid expansion of the money supply that vastly outstrips economic growth, along with a shortage of dollars that has left many firms unable to import raw materials or machine parts.

Wall Street analysts, local economists and opposition leaders have increasingly questioned the bank's autonomy, noting partisan language in statements, a reduction in available information and delays in releasing indicators.

(Reporting by Alexandra Ulmer; Editing by Andrew Cawthorne and Ken Wills)