(Adds context, details on price increases in June)
BUENOS AIRES, July 13 (Reuters) - Argentine monthly consumer prices rose 3.1 percent in June, the government said on Wednesday, easing from last month's figure but still above market forecasts as the government fights to tame one of the world's highest inflation rates.
The official reading - the second time statistics agency Indec has reported inflation data since Mauricio Macri became president in December 2015 - compared to last month's figure of 4.2 percent and a Reuters forecast of 2.5 percent.
Macri had shut down the publication of economic statistics during a revamp of Indec after his leftist predecessor Cristina Fernandez oversaw years of data widely viewed as false.
Indec did not publish an annual inflation figure for Latin America's No. 3 economy, but last month the finance minister forecast year-end 2016 inflation at around 40 to 42 percent, likely one of the world's highest rates.
Macri's slashing of subsidies and lifting of currency controls at the start of his term put new pressures on prices for everything from heating fuels to imported goods.
But the president has promised Argentines facing weak job prospects and stagnant wages that they will begin to see the results of his free-market reforms in the second half of 2016, including relief from booming prices that have especially hurt the poor.
Indec said price increases in June were driven by a 7.1 percent rise in costs for housing and basic services, and a 7 percent increase in prices for medical care. The agency tracks prices in the greater Buenos Aires area. (Reporting By Walter Bianchi, Editing by Rosalba O'Brien and Jeffrey Hodgson)