The number of people filing initial applications for U.S. state unemployment benefits rose slightly last week, while a monthly average level of applications fell to a 42-year low, the government reported Thursday, indicating a healthy labor market. Jobless claims increased 1,000 last week to 260,000, a level near lows set in late 1973, the Labor Department said. It was the 34th consecutive week that claims were below 300,000, a level associated with a fairly healthy jobs market. The four-week moving average of jobless claims—a less volatile measure considered a better gauge of labor-market trends—fell 4,000 to 259,250, the fewest since December 1973. The very low level of layoffs suggests the labor market remains in good health, despite a recent sharp slowdown in job growth. Economic growth slowed sharply in the July-September quarter, but that has not caused widespread layoffs, though some big companies have announced job cuts. The jobless-claims report showed the number of people still receiving unemployment benefits fell 37,000 to 2.14 million last week, the lowest level since November 2000.