WASHINGTON — The latest evidence that manufacturers are helping lead the economic recovery emerged today in a report that industrial production posted its seventh straight increase in January.

The report from the Federal Reserve showed gains in all three major categories: manufacturing, mining and utilities. It was the first such collective show of strength since August 2009. Manufacturing output rose 1 percent, led by a nearly 5 percent gain in auto production.

Manufacturing has been a major contributor to the early stages of the economic rebound. In the fourth quarter, for example, roughly two-thirds of growth came from a burst of manufacturing activity. Factories have been churning out goods for businesses that had let their stockpiles dwindle as a way to save cash.

A separate sign of strength came today in a Commerce Department report on housing construction. Home building posted a better-than-expected increase last month. Activity reached its highest point in six months.

Construction rose 2.8 percent to a seasonally adjusted annual rate of 591,000 units. That was better than the 580,000 annual pace economists were forecasting. Applications for building permits, a gauge of future activity, fell 4.9 percent to a rate of 621,000.

That followed two months of sharp increases.

The construction gains raised hopes that the industry is starting to sustain its recovery from its worst slump in decades. Still, analysts noted that most of the strength came from a jump in the volatile sector of apartment buildings. The much larger single-family category rose only slightly and didn’t make up for a sharp decline in December.

Overall housing activity remains sluggish. And economists cautioned that a housing recovery could stall if the government’s tax credits for home buyers expire as scheduled at the end of April. They also noted that the gains in industrial production, though encouraging, may provide only limited benefit to the broader economy.

“Unfortunately, activity in other sectors of the economy, such as housing and services, is still relatively weak,” Paul Ashworth, an economist at Capital Economics, wrote in a research note. “The problem is that the factory sector is now such a small part of the overall economy that the wider impact will be modest.”

The increase in housing construction last month was led by a 10 percent jump in activity in the Northeast and an 8.9 percent increase in the West. Construction was up a smaller 1 percent in the South and 3.2 percent in the Midwest.

The strength in January pushed construction activity up by 21.1 percent from the pace in January 2009. But it still remains well off the peak levels of the boom years in 2005 and 2006.

Construction of single-family homes rose by 1.5 percent to a seasonally adjusted annual rate of 484,000. Far stronger was building of multifamily units. It surged 9.2 percent to an annual rate of 107,000 units.

On Tuesday, the National Association of Home Builders said its housing market index rose by two points to 17 in February, after having fallen for two months.

That increase in sentiment was likely influenced, in part, by a report this month that the nation’s unemployment rate fell in January to 9.7 percent — still high, but lower than the 10 percent rate in December.

In addition, mortgage rates are hovering around 5 percent, pushed down by a Federal Reserve program to buy mortgage-backed securities. And builders say they are also seeing a boost in the demand for homes coming from a government stimulus program. That program provides tax credits of up to $8,000 for first-time home buyers and up to $6,500 for current homeowners who decide to move.

But private economists worry that the gains in housing could falter if mortgage rates begin to rise once the Fed withdraws its support and once the tax credits expire.