Making her first public remarks since the story broke on Sunday, Ms Gillard says she won't be making any other comments about the incident.
"It's not my intention to make any comment about that matter," she told reporters in Launceston.
"The only thing I want to say is this: both I and my family have been overwhelmed by the outpouring of support for us since the death of my father.
"From the bottom of my heart I'd like to thank Australians in their tens of thousands who have been so warm and so supportive at what has been a very difficult time for us."
Ms Gillard later declined to respond to several question on the affair, but did say: "I haven't spoken to Mr Jones and I don't intend to."
Jones told a Sydney University Liberal Club function last month that Ms Gillard's father John "died of shame" over his daughters political "lies".
