WASHINGTON — Americans’ incomes rose last month by the most in nine months, a hopeful sign for the economy after a year of weak wage gains. But consumer spending was flat.

Incomes rose 0.5 percent, the Commerce Department said today. It was the strongest increase since a similar gain in March.

Consumer spending was unchanged. That followed weak gains of 0.1 percent in both October and November.

The report underscored the challenge facing the economy in 2012. Unless incomes grow more rapidly, consumers will be forced to cut back further on spending. That would slow growth and result in less hiring.

After-tax incomes adjusted for inflation rose 0.3 percent in December. For the year, inflation-adjusted incomes rose 0.9 percent, just half the modest 1.8 percent rise in 2010.

The government reported Friday that the economy grew at an annual rate of 1.7 percent last year — roughly half the growth of 2010. It was the weakest showing since the economy contracted 3.5 percent in 2009.

Consumer spending for the year rose a modest 2.2 percent, only slightly higher than the 2 percent gain in 2010. But Americans dipped into their savings last year to finance some of the growth in spending last year.

Consumer spending is closely watched because it accounts for 70 percent of economic activity.