BUENOS AIRES, July 19 (Reuters) - Argentina's central bank left its 35-day reference interest rate unchanged at 30.25 percent on Tuesday for the second straight week, noting a recent rise in core inflation and warning of second-round impacts.

The central bank said it still believes inflation is easing and expects consumer price rises to slow to its goal of 1.5 percent per month in the fourth quarter, from 3.1 percent in June and 4.2 percent in May.

The central bank left the key interest rate unchanged last week after nine consecutive cuts, in the first sign it might be worried about inflation cooling as quickly as it hoped.

The cost of public services has shot up since center-right President Mauricio Macri slashed subsidies for utilities earlier this year, prompting public outrage and legal disputes that have suspended some of the hiked tariffs.

Core inflation in metropolitan Buenos Aires crept up to 3.0 percent in June from 2.7 percent in May, the central bank said, adding that the first report on prices in a district in the country's interior showed a drop in core inflation.

"Core inflation figures in the Buenos Aires metropolitan area suggest possible second-round effects, albeit limited, from the adjustments to tariffs," the bank said in a statement.

National statistics agency Indec has yet to report an annual inflation rate since the agency underwent reforms earlier this year.

The central bank, which must also weigh an economy that likely shrank in the second quarter, said it would exercise caution to keep its anti-inflationary bias in monetary policy and to contain second-round impacts.

(Reporting By Mitra Taj; Editing by Jonathan Oatis)