Greenspan told the Senate committee on the budget that the economy underwent a "significant cyclical adjustment" last year, worsened by the Sept. 11 attacks.
"But there have been signs recently that some of the forces that have been restraining the economy over the past year are starting to diminish and that activity is beginning to firm," Greenspan said.
Economic data from retail sales to jobless claims to manufacturing activity released in the past couple of weeks have been better than analyst's expected.
Greenspan, however, urged lawmakers considering fiscal measures to stimulate the economy to be mindful of the pressures that will be on budgets in the future.
The Senate is scheduled to begin debating a $69-billion stimulus package, an effort that had stalled amid partisan bickering. The package includes tax cuts for new business investment, rebates for low-income workers, extended unemployment benefits and more federal aid to cash-strapped states.
That Democrat-backed plan is considerably less ambitious than the $200 billion multiyear plan backed by President Bush and congressional Republicans.