New unemployment claims fell to a three-year low in the most recent week, adding to signs of a long-awaited improvement in the labor market, after last Friday's government report showed the best monthly job creation figures in four years. Initial weekly claims posted an unexpectedly sharply decline to 328,00 in the week ended April 3. That was 14,000 less than in the previous week, and much better than economists' consensus estimate for 340,000 claims. In addition, the four-week moving average -- thought to be a more accurate indicator -- fell to a four-year low of 336,750. The better-than-expected weekly figures follow nonfarm payroll figures showing that the economy added 308,000 jobs in March. The surprisingly strong job growth in March was also accompanied by healthy upward revisions in job gains for the previous two months. Weekly jobless claims have been below 400,000 -- thought to be the dividing line between growth and contraction in the labor market -- for about five months now. That indicator, along with others, had led economists to predict a pickup in job creation, which, prior to the March figures, had been unusually slow to materialize in the current economic recovery.