SAN FRANCISCO — Apple is working to make its iPhone and other gadgets smarter, responding to competitors’ recent moves by building more artificial intelligence into its Siri digital assistant, photos, maps and other online services.

The tech giant kicked off its annual software conference by announcing new software features for the Apple Watch and Apple TV, as well, while unveiling a new design for the Apple Music service. It’s also extending Apple Pay to the web, so users can pay for purchases made on their Mac computers using the fingerprint authorization on their iPhone or Apple Watch. Most of these new features won’t arrive until this fall.

At a time when sales of its flagship iPhone are slowing, Apple seemed determined to show that it can make its gadgets indispensable, or at least as useful as its competitors’ products.

Thinking fast and slow

Still, the tech giant is taking a cautious approach to integrating computer intelligence into its online services. While Apple is opening its text messaging service to outside app-builders, for instance, Apple made no mention of adding the kind of intelligent programs, or “chatbots ,” that competitors are all rushing to build into their messaging platforms.

Apple executives also stressed their efforts to safeguard users’ privacy even while providing recommendations and suggestions based on individual user information. The company says it’s committed to keeping most user data encrypted on individual iPhones or other devices, rather than uploading information to process on Apple’s servers.