Despite U.S. incomes rising at the end of the second quarter, American consumer spending fell in June by 0.1 percent from the month before, the Commerce Department said on Tuesday.

Commerce said incomes rose 0.5 percent in June but spending fell for the second straight month.

The figures suggest that in the third quarter U.S. consumer spending -- which accounts for about 70 percent of the nation's economic activity -- will be modest at best.

"Even if real spending rebounded by 0.2 percent month-on-month in each month of the third quarter, annualized real consumption growth in that quarter would still be 1.4 percent. If it rose by 0.1 percent month-on-month each month, it would be only 0.6 percent," Paul Dale, an analyst at Capital Economics, said in a report on Tuesday.