The row began on Friday when Phillips was asked at a press conference in New York whether Oracle would consider buying Salesforce.com following the acquisition of Siebel.
"In this case I think it would be much more fun to crush them," he replied. "We see a lot of ways to compete with them. We will try that for a while."
But the answer has drawn a fierce response from Salesforce.com, which has shown very strong growth in the customer relationship management market with its on-demand service.
"We welcome recent reports of Oracle's aim to 'crush' our company," said Chris Boorman, vice president of marketing at Salesforce.com EMEA.
"Competition is good and, when one of the largest technology companies in the world sees you as such a threat that the president himself needs to resort to macho posturing in public, it feels really good.
"On-demand computing is the future, and we invite all companies to come and obtain the value that our 308,000 subscribers are already receiving."
At the same time Salesforce.com chief executive Marc Benioff piled on the pressure in an internal email, in which he offered a $5,000 bounty to former Siebel employees who want to join his company.
"Following the acquisition of Siebel by Oracle many existing Siebel employees may be concerned about their career prospects, [and] we want to offer them an alternative to an environment of declining commissions, confused customers and uncertainty around career viability," he wrote.
Salesforce.com will be holding recruitment fairs in Boston and San Mateo on 19 October.
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