Greenspan made his comments at the start of the Federal Reserve Board's annual economic symposium, which is devoted this year to the economic impact of global demographic changes.
But the issue is also a backdrop to the presidential election campaign. Bush and many Republicans are promoting the idea of replacing part of the traditional Social Security system with private savings accounts.
The Democratic nominee, Senator John Kerry, has opposed such plans and has vowed to ensure that benefits are not reduced in the future.
Neither candidate has addressed the long-term challenges in any detail. Most analysts contend that the looming financial shortfalls of Social Security are relatively modest and could be addressed by incremental changes to benefit formulas and a gradual delay in retirement ages.
The problems confronting Medicare are expected to be far more severe, because costs have been rising rapidly per person at the same time that the population of retirees has been increasing.
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