The number of people filing initial applications for U.S. state unemployment benefits rose slightly last week, while the four-week average of claims fell to its lowest level in more than 40 years, the government reported Thursday, indicating a strengthening labor market. The Labor Department said jobless claims increased 3,000 last week to 259,000, not far above levels last week in late 1973. It was the 33rd consecutive week that claims were below 300,000, a level typically associated with an improving jobs market. The four-week moving average of claims—a better gauge of labor-market trends because it smoothes weekly volatility—fell 2,000 last week to 263,250, the lowest level since December 1973. The measure has fallen by more than 9,000 between September and October, suggesting an acceleration in job gains this month. At current levels, there is not much room for jobless claims to fall further, and the very low level of layoffs suggests the labor market remains healthy, despite a recent sudden slowdown in job growth. The claims report showed the number of people still receiving unemployment benefits rose 6,000 last week to 2.17 million. The four-week moving average of so-called continuing claims was the lowest since 2000, suggesting further declines in the national unemployment rate.