* Weekly jobless claims rise 4,000 * Four-week average increases 2,750 * Claims show no deterioration in labor market conditions * Mid-Atlantic factory activity slows in April By Lucia Mutikani WASHINGTON, April 18 (Reuters) - The number of Americans filing new claims for unemployment benefits rose last week and factory activity in the nation's Mid-Atlantic region cooled in April, further signs of a moderation in economic growth. Underscoring the softening growth outlook, another report on Thursday showed a gauge of future economic activity fell in March for the first time in seven months. They were the latest data to indicate a step-back in the economy after a brisk start to the year as tighter fiscal policy began to weigh. "The evidence is mounting that the economy lost momentum in March and that has carried to April," said Ryan Sweet, a senior economist at Moody's Analytics in West Chester, Pennsylvania. Economic data for January and February suggested that growth accelerated in the first quarter after activity almost stalled in the final three months of 2012. But in a replay of the prior two years, the economy appeared to have hit a speed bump at the end of the quarter, with data ranging from employment to retail sales and manufacturing weakening significantly in March. Initial claims for state unemployment benefits rose 4,000 to a seasonally adjusted 352,000, the Labor Department said. The four-week moving average for new claims, a better measure of labor market trends, rose 2,750 to 361,250. While claims rose last week, they were still at levels economists normally associate with average monthly job gains of more than 150,000. That helped ease concerns of a deterioration in labor market conditions after an increase in nonfarm payrolls in March was the smallest in nine months. "Labor market conditions still appear to be grinding forward, but pushing against the weight of a slowing economy and subdued confidence," said Jim Baird, chief investment officer at Plante Moran Financial Advisors in Kalamazoo, Michigan. DOWNBEAT OUTLOOK In separate report, the Philadelphia Federal Reserve Bank said its business activity index fell to 1.3 in April from 2.0 in March. A reading above zero indicates expansion in the region's manufacturing. It came on the heels of data this week showing a sharp slowdown in factory activity in New York state in April and a dip in national manufacturing output last month. Details of the survey, which covers factories in eastern Pennsylvania, southern New Jersey and Delaware, showed weakness. Measures of factory employment and new orders contracted. Inventories fell sharply after being flat in March, an indication that stock accumulation will not contribute to growth in the second quarter. Inventories are expected to have significantly boosted output in the first three months of 2013. "This report has to raise some concerns that the nation's manufacturing sector may be starting to feel the impact of the higher taxes on households and the cutbacks in government spending," said Joel Naroff, chief economist at Naroff Economic Advisors in Holland, Pennsylvania. A third report supported views the economy was again headed for a soft patch this spring. The Conference Board said its Leading Economic Index slipped 0.1 percent last month, the first decline since August. The data provides ammunition for the Federal Reserve to maintain its aggressive policy easing, despite a rift among policymakers on continuing asset purchases. "Growth is continuing, but a spring slowdown looks to be in place. The numbers support the view of many at the Fed that the end of the liquidity surge is nowhere in sight," said Naroff. On Thursday, Minneapolis Fed President Narayana Kocherlakota said the purchases of government bonds and mortgage-backed securities were necessary to boost employment but said they would cause financial market instability for years. U.S. stocks ended down for the third day this week on the downbeat data, with the Standard & Poor's 500 index breaking below its 50-day moving average for the first time this year. Treasury debt prices gained slightly, while the dollar fell marginally against a basket of currencies. Last week's claims data covered the survey period for April nonfarm payrolls. Claims increased 11,000 between the March and April survey periods. Given recent volatility because of the early Easter and school spring breaks this year, claims are probably not useful in trying to gauge April payrolls. Employers added 88,000 workers to their payrolls last month after a solid 268,000 increase in February. While job growth has slowed in line with the overall economy, economists said March's meager gains overstated the labor market's weakness. "We see nothing in the jobless claims data to either suggest that job growth has deteriorated further since March or even to support the view that March's payroll gain represents a new trend," said John Ryding, chief economist at RDQ Economics in New York.