While dads across the world were celebrating the special day last month (Jun15), musician Bill Hudson was called out by his son Oliver, who took to social media and posted an old family shot of himself as a kid with his dad and sister Kate, adding the caption: "Happy abandonment day".

Now the Almost Famous actress has dissed her dad again during a candid chat with adventurer Bear Grylls on the season premiere of U.S. show Running Wild With Bear Grylls.

As the Brit and his celebrity sidekick were setting up camp during a trek through the Dolemites mountain range in Italy, Grylls asked the actress about her relationship with her mother Goldie Hawn's longtime boyfriend Kurt Russell, who Hudson refers to as "Pa".

She said, "Kurt's not my real dad but Kurt was amazing. He raised us from the age of three. Only until (sic) I got older did I really look at it and go, 'That's a real taking on for a man...'"

Her comment prompted Grylls to state, "That kind of makes him your real dad."

Hudson responded, "He's my dad. He's what I know."

The actress then added she no longer "has a relationship" with her biological dad, Bill, adding, "It just never really panned out that way."

Bill Hudson divorced Oliver and Kate's mum Goldie Hawn in 1980.

During the camp chat, mother-of-two Hudson also opened up about her future marriage plans. The star, who was previously married to rocker Chris Robinson and engaged to Muse frontman Matt Bellamy - the fathers of her two sons - admitted she would like to wed again, but added, "I wanna do it when it feels right. I see it as something that should be a real celebration of how much you wanna be committed to someone and I think that takes time."

Hudson's overnight Italian adventure aired on TV in America on Monday (13Jul15).