(Adds detail on June debt, funding data) BRASILIA, July 28 (Reuters) - Brazil’s federal public debt rose 3% in June from the month before to 5.33 trillion reais ($1.03 trillion), the Treasury said on Wednesday, adding that its emergency cash buffer surged to a new high of 1.17 trillion reais. In the month that saw the central bank raise official borrowing costs for a third straight meeting, the Treasury also said the cost of servicing Brazil’s growing domestic debt pile edged up to its highest in a year. “The domestic scenario in June was marked by monetary policy expectations. The increase in the Selic rate ... led investors to adjust bets on the (future) trajectory of interest rates,” the Treasury said in a statement. The average cost of servicing new domestic debt issued in the 12 months through June rose to 5.8% from 5.5% in May, the Treasury said. That is the highest in over a year, and up significantly from 4.4% at the end of last year. The average cost of servicing the overall domestic debt stock in the 12 months through June rose to 7.7% from 7.6%, also the highest in a year, the Treasury said. The average cost of servicing the overall public debt stock including foreign debt in the year through June, however, fell to a fresh historical low of 7.2% from 7.3% in May. The Treasury’s liquidity cushion, essentially an emergency cash buffer, rose to 1.17 trillion reais from 1.04 trillion reais, the highest on record. In nominal terms, that was up 12% from May and 70% higher than a year ago. The Treasury noted that debt coming due in the next 12 months is estimated at 1.18 trillion reais. $1 = 5.17 reais Reporting by Jamie McGeever; editing by Jonathan Oatis and Steve Orlofsky Our Standards: The Thomson Reuters Trust Principles.