Apple plans to tighten its online security measures to reduce the chances of its users being victimized by intrusions like the ones that stole nude photos from actress Jennifer Lawrence and other celebrities.

CEO Tim Cook told The Wall Street Journal in a story published Friday that Apple Inc. will use email and push notifications to alert the hundreds of millions of people using its services when there has been an attempt to restore their iCloud data on a new device, change an account password or log on to an account with a new device. Previously there were no notifications for restoring iCloud data, but users did receive an email when someone tried to change a password or log in for the first time from a new device.

Apple expects to start sending the additional notifications in two weeks. The iPhone maker said the new security will allow users to change passwords to reclaim control of an account or notify Apple’s security team about a potential problem.

An Apple spokesman confirmed the report Friday but declined to comment further than what was said in the interview.

Apple is also urging users to ensure they have complex passwords that are difficult to guess and are enabling a feature known as two-factor authentication that requires a numeric code sent to a phone to gain access to an account.

The security clampdown comes just a few days after Apple acknowledged computer hackers broke into the accounts of Lawrence and several other stars whose revealing photos were posted online during the Labor Day weekend. The Cupertino, California, company blamed the security breakdown on the intruders’ ability to figure out passwords and bypass other safeguards.

The embarrassing episode raised doubts about Apple’s online security at a time when the company is preparing to introduce several services that will seek to vacuum up even more information about people’s lives and finances. When Apple unveils its next iPhone at a Tuesday event in Silicon Valley, Cook also is widely expected to provide more details about previously announced services designed to help people manage their health and home appliances. Analysts also believe Apple will include a digital wallet for making payments on the iPhone and, possibly, a long-awaited smartwatch, too.

As part of its efforts to reassure users, Apple has emphasized that it found no evidence of a widespread problem in iCloud or its Find my iPhone service. Instead, the affected celebrity accounts were targeted by hackers who had enough information to know the usernames, passwords and answers to personal security questions designed to thwart unauthorized entries, according to Apple.

Knowing this crucial information would enable an outsider to break into Apple accounts, including iCloud, and many other types of online accounts. The digital burglaries, though, probably would have been thwarted with two-factor authentication.

Apple’s stock added 65 cents to $98.74 in Friday’s early afternoon trading.