Tweed sparked off the argument by mocking Natasha Giggs's alleged eight-year affair with her husband's footballer brother Ryan Giggs. Natasha and Rhodri Giggs were spotted together earlier this week, indicating that they had reunited.
Tweed tweeted: "How has giggs brother taken her back after an 8 year affair. One word come to mind. #mug (sic)."
Rhodri Giggs later responded: "mug.... Hopefully we bump into each other then we'll see who the mug is...little f****t."
Natasha Giggs waded into the argument by writing: "of all the people I would've thought u would not believe everything u read #mug #jogon."
Rhodri Giggs later suggested that he and Tweed take part in a charity boxing match to settle their dispute.
The model and recent Celebrity Big Brother evictee recently had a Twitter argument with Imogen Thomas over their alleged affairs with the Manchester United player.
Jack Tweed pleaded guilty to common assault outside of an Essex nightclub last year.
> Natasha Giggs blasts kiss-and-tell: 'I don't care, I'm moving on'