By Gabriel Araujo

SAO PAULO (Reuters) -Annual inflation in Brazil slowed further in early June, hitting its lowest in nearly three years as the central bank signaled it may start cutting interest rates at its next meeting if consumer prices stay tame.

In Latin America's largest economy, 12-month inflation reached 3.4% in mid-June, data from statistics agency IBGE showed on Tuesday, slightly above market expectations of 3.36% but a deceleration from 4.07% in May and the lowest since September 2020.

Analysts expect Latin America's major central banks, which have led some of the most aggressive tightening over the last two years, to lead the world on interest rate cutting.

Brazil's inflation "continued to fall rapidly during Q2 and inflation expectations are now under control," said Pantheon Macroeconomics' Andres Abadia, noting that would allow the central bank "to cut rates soon."

Earlier in the day, Brazil's central bank did confirm that a majority of its monetary policy committee see a rate cut in August as possible if disinflation continues.

Annual inflation is now within this year's upper target range of 3.25%-4.75%, although an uptick is expected from July because of unfavorable base effects.

The bank's dovish stance came after it decided last week to keep benchmark rates at a six-year high of 13.75% for a seventh consecutive meeting. That move upset government officials who see it as hindering economic growth.

"It's hard to argue against the start of an easing cycle in August," said Capital Economics' chief emerging market economist William Jackson. "We've now penciled in a 25-basis-point cut to 13.50% at the next meeting."

Brazil's IPCA-15 consumer price index rose 0.04% in the month to mid-June, IBGE data showed, down from 0.51% in the previous month. The index had been expected to fall 0.01%, according to the median forecast in a Reuters poll.

The monthly rise was driven by higher housing prices and personal expenses, the agency said, which was largely offset by a drop in food and transportation costs.

The country's new leftist government, which won last year's election on pledges to work to bring down consumer prices and boost economic growth, has welcomed the latest news.

"It is a clear sign that the economy is being rebuilt," Institutional Relations Minister Alexandre Padilha said. "Everything is in place for our country to start lowering interest rates."

(Reporting by Gabriel Araujo; Editing by Steven Grattan, Angus MacSwan and Emelia Sithole-Matarise, David Gregorio)