Oracle co-founder Larry Ellison on Thursday threw jabs at e-commerce giant Amazon because it is trying to get at their market share in the cloud.

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The two tech behemoths have been engaged in a recent war of words over the performance of Oracle's database software and cloud tools.

Amazon recently announced plans to move off Oracle by 2020, which caused an outage on Prime Day in one of its biggest warehouses, according to an internal report.

“Amazon now has kind of been the No. 1 brand in infrastructure cloud computing,” Ellison said during an exclusive interview with Maria Bartiromo.

“Let me tell you an interesting fact: Amazon does not use [Amazon web services] to run their business,” he added. “Amazon runs their entire business on top of Oracle, on top of the Oracle database. They have been unable to migrate to AWS because it’s not good enough.”

Even so, Oracle has faced its fair share of challenges in the cloud.

“We didn’t get our database to the cloud quickly enough,” said Ellison. “So, if you wanted a cloud database, you had to go to Amazon for a database and then you’re able to go to Microsoft for a database. It took us a while for us to build a secure cloud. It’s really hard to build a secure cloud.”

Amazon currently has a 33 percent share of the cloud market, followed by Microsoft, which has gained ground recently, climbing from 7 percent to 13 percent.

And according to Ellison, Oracle continues to maintain a dominating position in managing most of the world’s data.

“We think we’re there now. We have by far and away the best the database in the world. Nothing is close,” he said. “We show a series of benchmarks where we’re 10 times faster than Amazon. More importantly, we’re 10 times cheaper to run the same exact thing than Amazon on our database.”