Markets are eager to see if Washington is determined to pursue fiscal tightening that could help offset structural problems in the US economy which have taken the dollar to record lows versus the euro last year.
"People are looking at Greenspan's comments and thinking maybe this is not the end of the dollar decline," said David Mann, foreign exchange strategist at Standard Chartered in London. "Short term people are also realising that Greenspan's positive message could be much longer term...and the fact is that the current account deficit is still widening," he added.
The dollar hit its highest levels against the euro since November 5, 2004 at $1.2828 on Monday, but fell to $1.2858 at 1300 GMT to trade almost steady on the day.
The dollar also stabilised against the yen to trade at 104.22 after hitting an intra-day high of 104.65 yen.
The Japanese currency had a weak bias after fresh comments from Chinese policymakers on Monday reinforced similar statements made over the weekend and further dampened speculation of a near term yuan revaluation.
China's central bank governor Zhou Xiaochuan said much preparation would be needed before there could be any changes to China's foreign exchange regime.
Greenspan spoke again on Monday during a speech to accept an honorary degree from the University of Edinburgh, but steered clear of current economic and monetary policy issues.
On Friday, Greenspan said market forces and tighter US fiscal policy should stabilise and may cut the current account deficit.
This surprisingly optimistic view helped ease persistent worries that the dollar could suffer if the US economy failed to attract enough foreign cash to plug the external shortfall.
But with the current account still looming large and many analysts questioning any fiscal tightening that Washington may propose, investors thought dollar weakness could still return.
Some analysts said that even drastic domestic spending cuts would have to be endorsed by Congress against fierce Democrat opposition.