The TV spots feature shoppers who are on the lookout for a laptop under $1,000. They consider Apple's Macintosh models but dismiss them because they are too expensive.
Kevin Turner, Microsoft's chief operating officer, said that Apple's legal team had called him and asked him to cancel the ads because Apple had lowered the prices on some of its machines.
Turner, speaking at Microsoft's Worldwide Partner Conference in New Orleans this week, said: "Two weeks ago we got a call from the Apple legal department saying, 'Hey, you need to stop running those ads, we lowered our prices'.
"They took like $100 off or something. It was the greatest single phone call that I've ever taken in business.
"I did cartwheels down the hallway. At first I said: 'Is this a joke? Who are you?'
"We're just going to keep running them and running them and running them."
Microsoft's latest ads follow its 'I'm a PC' ads, launched last year, which were created in response to Apple's 'Mac vs PC' ads, which feature a geeky PC guy unable to keep up with the "hip Mac user".
Prior to its 'I'm a PC' ads, the software giant launched a $300m ad campaign, featuring comedian Jerry Seinfeld and Microsoft's chairman Bill Gates. The ads received a critical mauling across the blogosphere.