The euro and gold lost ground after US jobless claims fell, but gained later when Greenspan's comments were repeated on Thursday.
A weaker US currency supports dollar-priced gold, making it cheaper for those holding other currencies.
"With the dollar remaining under pressure, partly as a result of...comments from Greenspan, the risks for prices probably lie on the upside in the short term," HSBC metals analyst Alan Williamson said.
The euro was last at $1.3056, up from $1.3030 in late US trade on Wednesday.
Greenspan provided no surprises on Wednesday as he reiterated that the US economy was expanding at a healthy pace and that the fed funds rate remained low in real terms despite recent rises.
Analyst James Moore of TheBullionDesk.com said in a report that gold could be edging eventually to $445 - almost $10 short of the 16-1/2-year peak of $456.75 scored in December.
"With the dollar seeming back under pressure gold will now look to work higher," he said.
In other precious metals spot silver firmed in line with gold to $7.30/7.33 from $7.24/7.27 in New York on Wednesday.
Spot platinum moved up to $862.00/867.00 from $854.00/858.00, rallying from pressure seen in the Tokyo futures market overnight.
Global No 2 platinum producer Implats posted flat headline earnings for the first half on Thursday and said growth was unlikely in the second six months, hitting shares.
Analysts said higher metals prices were offset by a buoyant rand currency that cuts export revenues and which also resulted in a bigger-than-expected foreign exchange loss.
Platinum hit a 24-year peak last year at $942 per ounce. Palladium was steady at $179.00/183.00 from $178.00/183.00 previously.