In an op-ed article in The New York Times earlier this month, Pichai said that "privacy cannot be a luxury good offered only to people who can afford to buy premium products and services".
Pichai did not name Apple directly, but people in the know do not doubt which company he was referring to.
In an interview with The Independent on Monday, Federighi said he doesn't "buy into" the criticism that Apple was turning privacy into a luxury good.
"I think it's a deeper issue than then, what a couple of months and a couple of press releases would make. I think you've got to look fundamentally at company cultures and values and business model. And those don't change overnight," Federighi was quoted as saying by The Independent on Monday.
"And of course, we love, ultimately, to sell Apple products to everyone we possibly could certainly not just a luxury, we think a great product experience is something everyone should have. So we aspire to develop those," he added.
The privacy battle between Apple and Google is unlikely to slow down, The Verge reported.
As Apple does not rely on selling ads for it revenue, Apple can use privacy protection as a key selling point for its products.
This incentivises the company to keep volleying back at Google, said the report.
( With inputs from IANS )