The Aston Villa central defender limped off at the end of Ireland's defeat to Croatia but rejoined the group after sitting out Monday's session
Dunne, 32, sat out training on Monday due to foot blisters following Ireland's defeat in their opening match against Croatia on Sunday.
Darron Gibson, who had a scan on a thigh problem on Monday, also took part in the session at the Gdynia Municipal Stadium.
Giovanni Trapattoni's side are bottom of Group C following their loss and have world champions Spain to play on Thursday.
A defeat would see Ireland eliminated after only two matches. Italy and Spain drew in the other Group C clash on Sunday.