The United States is likely to see 10-percent unemployment levels "for a while," former U.S. Federal Reserve Chairman Alan Greenspan said Sunday.

However, speaking on the ABC program "This Week," Greenspan also said the U.S. economy is approaching a time when continuing job losses would end.

"I think we're getting close to (the end of job losses)," Greenspan said. "But remember, the end of the job loss is not the same thing as if the unemployment rate is going to start down. My own suspicion is that we're going to penetrate the 10 percent barrier and stay there for a while before we start down."

Greenspan also sounded a cautious note on the idea of a second package of government economic stimulus spending.

"I think the focus has got to be on trying to get the economy going, but you also have to be careful that in trying to do too much you can actually be counterproductive," he told ABC.