A spiraling U.S. trade deficit over time can pose a risk to the U.S. economy, while at the same time the insatiable foreign demand for dollar holdings will eventually fall as investors diversify, Federal Reserve (search) Chairman Alan Greenspan (search) said on Friday in remarks that impacted the dollar and world markets.

Greenspan told a banking conference in Frankfurt that the U.S. should cut its record budget gap to help narrow the shortfall in its current account and avoid a need to offer higher rates of return to retain foreign investment and painful economic consequences.

The Fed chief also said an eventual desire by foreign investors to cut the risk of holding too many dollars may lead them away from U.S. assets or lead them to seek higher rates of return. He warned this would elevate the cost of financing of the U.S. current account deficit and render it "increasingly less tenable."

The dollar slumped across the board, plunging to four-and-a-half-year lows against the yen on Friday after the remarks. European shares barely clung to 28-month peaks as the dollar renewed its slide.

"We see only limited indications that the large U.S. current account deficit is meeting financing resistance," Greenspan said. "Yet, net claims against residents of the United States cannot continue to increase forever in international portfolios at their recent pace."

The broadest measure of trade, called the current account deficit (search), swelled to an all-time high of $166.2 billion in the second quarter of this year, the most recent period for which this information is available.

"Current account imbalances, per se, need not be a problem, but cumulative deficits ... raise more complex issues," Greenspan said.

The dollar's slide has been good for U.S. manufacturers because it makes their goods less expensive in foreign markets. But the corresponding rise of the euro makes European goods more expensive in foreign markets.

Greenspan, in his speech, did not specifically discuss the value of the dollar. Although he said that forecasting exchange rates "has a success rate no better than that of forecasting the outcome of a coin toss."

In his speech, Greenspan also didn't discuss the future course of interest rate policy in the United States.

Wanting to keep inflation from becoming a danger to the economy, Fed policy-makers last week boosted short-term interest rates for a fourth time this year. The action left a key rate, called the federal funds rate, at 2 percent. The funds rate is the Fed primary tool for influencing economic activity.

Reuters and the Associated Press contributed to this report.