The original cut-off date was this month, but users now have until May 15 to take action.
The firm was criticised for sending the notification, which seemed to suggest changes to the data it would share with its parent company Facebook.
It said there had been "confusion" about its message.
Since the announcement and notifications went out across its platform, millions have downloaded alternative encrypted messaging apps such as Signal and Telegram.
WhatsApp is updating its terms and privacy policy
A WhatsApp spokesperson said: "As we’ve previously talked about, we’re updating our terms of service and privacy policy as we work to make WhatsApp a great way to get answers or help from a business.