Retirees tend to save more, he said, expressing hope that the large post-World War II baby boom generation will do the same.
Greenspan also implicitly urged actions to reduce the record federal budget deficit, but saying that "critical to national saving will be the level of government, specifically federal government saving."
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"Unless actions are taken," he said without specifying the actions, the deficit will become far worse as the share of the American population over age 65 grows from about 12 percent today to around 20 percent by 2035.
Greenspan also repeated his call for the nation to "engage in a long overdue upgrading of primary and secondary school education," as another way to enhance productivity.
The problems of supporting a growing elderly population are common throughout the industrialized world, where the ratio of older adults to younger adults has been rising for at least 150 years, he said.
The aging of the population slowed greatly with the baby boom that followed World War II, but picked up again as birth rates fell and life expectancy rose through the late 20th century.
U.S. working-age population is projected to grow more slowly in coming years, with the rate of increase falling from about 1 percent per year today to 0.25 percent per year by 2035, he said. Meanwhile, the baby boom generation is just a few years away from starting to claim federal retirement benefits.
"The relative aging of the population is bound to bring with it many changes to the economy of the United States -- some foreseeable, many probably not," Greenspan said. "Inevitably it will again require making difficult policy choices to balance competing claims."