"Oracle has been in the Linux business for a year now. With the Red Hat code all we did for the first year was fix bugs," he said.
"Now Oracle is growing a lot faster than Red Hat. Red Hat has been growing too because it is a growing market."
Ellison maintained that this week's launch of Oracle VM gave Oracle something that Red Hat could not match.
Oracle unveiled the Oracle VM virtualisation server on Monday based on the Xen open source technology. Red Hat has incorporated Xen into its Linux distribution.
Ellison also pointed out that Oracle had set up systems that would let Red Hat users switch to Oracle in a matter of minutes.
He also announced that the first Fusion applications would be released next year, although he refused to be drawn on when.
The first modules would be for sales force automation and the software would integrate totally with Oracle's ERP software.
In the much longer term Ellison said that Oracle would rewrite all its applications to include a version of Fusion. But he warned that this could take 10 to 15 years.
Ellison was introduced for his keynote by Billy Joel, who is performing at tonight's 30th birthday party for the company.
"I'm excited to be here," said Joel. "But considering how many car accidents I've had over the last few years I'm just excited to be anywhere."