Leo Apotheker, chief executive of Hewlett-Packard, said that his company will focus on three areas of leadership in the future: cloud computing, connectivity, and software.

HP is the world’s biggest technology company, but it hasn’t necessarily been the leader in those areas in the past. But Apotheker, speaking today about company strategy in San Francisco to analysts and press for the first time since he became CEO in November, said HP will build and operate its own “public cloud,” or a platform to deliver all kinds of services to businesses and consumers.

That cloud will interact with its customers’ own private clouds and provide the kind of high-interaction services that consumers have come to expect in the age of the internet for transactions such as e-commerce or digital distribution.

Apotheker said HP is prepared to securely deliver end-to-end services and technologies to make this happen. The public cloud platform will be interoperable, trusted, have its own app store, and work with the 100 million-plus WebOS devices that HP plans to ship in the coming years via its PCs, smartphones, tablets and printers.

“To be clear, we don’t need to own the big transactional platform,” he said, noting HP can partner to do that.

HP’s acquisition of Vertica Systems is an indication of where HP is going, and the company will have a new appliance on the market when that deal closes. HP announced the deal on Feb. 14, and it will provide HP with real-time analytics for “big data,” or huge databases for handling interactions with large numbers of consumers.

As for software, HP will offer software over the cloud in the form of software-as-a-service, as provided by rivals such as Salesforce.com. As an example, HP said it could apply all of the real-time analytics and customer information at hand to figure out the exact rate that a rental car company should apply to a customer who wants to rent a car.

Apotheker said that security is the key to ensuring cloud computing is safe. HP is the fifth-largest security information technology company in the world, and its focus is to provide a security backbone across a distributed infrastructure.

He said HP can handle operations for small, medium and large businesses itself. Or it can offer them components that they can mix and match together in a heterogenous environment. Or it can offer services and hardware that the businesses can operate.

“No company is better positioned than HP,” Apotheker said.

In a Q&A with reporters, Apotheker said elements of the cloud infrastructure are in place now and more will roll out during 2011 and 2012. The same goes for HP’s own app store. I asked Apotheker if HP will now compete with its own cloud-computing customers. He said the company will continue to partner with its current customers and will roll out the public cloud for those customers who are asking for that and will not do it themselves.

HP is playing catch-up in a big way in the cloud compared to rivals such as Rackspace and Amazon. But, he said, “We will catch up and we will talk to you about it when we do.”