* Consumer prices rise 0.5 percent in June * Core CPI rises 0.2 percent for second straight month * Report shows disinflation trend fading * Industrial production rises 0.3 percent in June By Lucia Mutikani WASHINGTON, July 16 (Reuters) - U.S. consumer prices picked up in June and underlying inflation pressures showed signs of stabilizing, keeping on course expectations the Federal Reserve will start reducing its bond purchases later this year. While inflation remains benign, the increase last month should help ease worries among some Fed officials that price pressures in the economy were too low. "Inflation is carving out a bottom. We are likely to see inflation tick up slightly in the second half of this year," said Ryan Sweet, a senior economist at Moody's Analytics in West Chester, Pennsylvania. "The modest acceleration is welcome news for the Fed." The Labor Department said on Tuesday its Consumer Price Index increased 0.5 percent, the largest gain since February, after nudging up 0.1 percent in May. A 6.3 percent surge in gasoline prices accounted for about two thirds of the increase. In the 12 months through June, the CPI advanced 1.8 percent, an acceleration from the 1.4 percent logged in the period through May and the largest increase since February. Stripping out energy and food, consumer prices increased 0.2 percent for a second straight month. That took the increase over the past 12 months to 1.6 percent, the smallest rise since June 2011. The core CPI had gained 1.7 percent in May. Although both inflation measures remain below the Federal Reserve's 2 percent target, the report showed signs of fading disinflation pressures, with medical care costs increasing after being subdued for the past two months. Prices for new motor vehicles, apparel and household furnishings also rose. The signs of stabilization offered by the monthly core measure fit in with Fed Chairman Ben Bernanke's assessment that a downward drift in the inflation rate was temporary. Bernanke said last month the central bank would likely later this year start cutting back the $85 billion in bonds it is purchasing each month to keep borrowing costs low. Economists expect the Fed to begin reducing the amount in September. "The lack of further slowing in core inflation on a monthly basis in the last two months helps keep Fed tapering on track," said Jim O'Sullivan, chief U.S. economist at High Frequency Economics in Valhalla, New York. BETTER GROWTH PROSPECTS While the year-on-year core CPI rate could slip further in coming months, it should reverse course as economic growth accelerates over the last half of the year, economists said. They expect a drop in unemployment to boost wage growth. That optimism about the economy's prospects was bolstered by a separate report from the Fed showing output at the nation's factories, mines and utilities rose 0.3 percent in June after a flat reading in May. The increase reflected a 0.3 percent rise in manufacturing output. Economists said it suggested some pickup in economic activity at the end of the second quarter. Growth in the April-June period is forecast at an annual pace of between 0.5 percent and 1.0 percent, far below the first-quarter's 1.8 percent rate. "If manufacturing growth is on the verge of accelerating into the second half of the year, this, along with solid gains in housing, should support growth in the second half of 2013," said John Ryding, chief economist at RDQ Economics in New York. Another report on Tuesday showed confidence among single-family home builders soared to a 7-1/2 year high in July, amid expectations of stronger sales and buyer traffic. U.S. financial markets were little moved by the data as investors awaited testimony Bernanke is set to deliver to Congress on the economy on Wednesday. Tepid growth has kept a lid on inflation pressures, but some pockets of pricing power are starting to emerge. Last month, owners' equivalent rent, which accounts for about a third of the core CPI, increased 0.2 percent after a similar gain in May. Apparel prices recorded their largest increase in nearly two years, while new motor vehicle prices rose after being flat in May. Medical care services rose 0.4 percent, the largest increase in a year. Medical care, which makes up about 10 percent of the core CPI, had been subdued in April and May. The cost of medical care commodities rebounded 0.5 percent, reversing the prior month's decline, as the price of prescription drugs increased. Tame medical care costs have been one of the key contributors to the low inflation rate over the past months. Economists cite a host of reasons for the lack of pressure on health care costs, ranging from the expiration of patents on several popular prescription drugs to government spending cuts that have cut payments to doctors and hospitals for Medicare. "We think the impact of these transitions has started to fade away and we expect that drug price inflation may start to pick up over the months ahead," said Ryan Wang, a U.S. economist at HSBC in New York.