The band's former frontman had served a legal writ against his sibling accusing his of releasing false statements about the end of the band, including a comment Liam didn't play the second night of their headlining slot at the music event in Chelmsford, England, in August 2009 because he was ill from drinking and alleging they had an earlier bust-up about his Pretty Green clothing range.
The 38-year-old singer has now withdrawn his legal action after the 44-year-old guitarist admitted his brother did have laryngitis before the scheduled concert and a doctor had told him to rest his voice.
Speaking in a webcast with comedian Matt Morgan, Noel said: "For the record, it is a fact that he was diagnosed with laryngitis and it is a fact that he had a doctor's note to prove it. I'd just like to say that if he gets offended by my opinions on such things then I apologise.
"It's all getting a little silly and out of hand and it's not very cool."
Liam - who has not spoken to his brother since the band split a few weeks after the cancelled V Festival performance, and didn't attend his wedding to Sara MacDonald earlier this year - was also convinced to stop the court action by their mother Peggy.
A source told The Sun newspaper: "Liam had spoken to his mum Peggy and she was upset by the whole episode.
"That was playing on his mind then he had a moment of realisation that Noel wasn't being vindictive - he was just being cheeky. It was an anger that had built up over two years because he was so angry Oasis was over.
"In the cold light of day he realised his brother was actually being quite calm about it all, and decided a legal battle was a bad idea. Hopefully that will draw a line under it all and everyone can move on."
Liam - who now fronts Beady Eye - has always vehemently denied he pulled out of the V Festival because he was ill from alcohol, branding Noel's comments a blight on his professionalism.
He previously said: "Those are big lies that I've got to clear up, the first one about me being hungover - I got diagnosed with laryngitis for the V festival, wasn't hungover. I do gigs when I've been hungover, I'm a Big Boy. I'm not going to cancel a gig because I've got a headache."
While Liam fronts Beady Eye, his brother is getting ready for the release of his first solo album 'Noel Gallagher's High Flying Birds'.