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Page, along with Google Chief Executive Eric Schmidt, spoke with reporters this week at the Allen & Co. conference, according to Reuters. Jobs was invited, but did not attend.
Page, on Thursday, said that Jobs' suggestion that Google was responsible for the animosity between the two companies by choosing to compete with the iPhone in creating its own Android mobile platform was "a little bit of rewriting history."
"We had been working on Android a very long time, with the notion of producing phones that are Internet enabled and have good browsers and all that, because that did not exist in the market place," Page reportedly said. "I think that characterization of us entering after is not really reasonable."
Schmidt added that he believes the market is large enough for both Apple and Google to thrive. He said most people incorrectly "assume that these are zero-sum games, which are battles to the death."
Schmidt noted that Apple and Google still have important partnerships. Google powers the Maps application found on the iPhone, and powers the native YouTube application as well. And it is also the default search provider on all iOS devices, including the iPod touch and iPad.
Schmidt also said that he believes that Chrome OS, set to arrive later this year, will appear on tablet PCs, and will compete with Apple's iPad.
Last summer, as both companies grew in competition, Schmidt resigned from the Apple Board of Directors. His departure was seen as necessary as Google and Apple now compete in numerous markets in the technology sector: Google's Android mobile operating system competes with Apple's iPhone; both companies recently made large mobile advertising acquisitions; Google's forthcoming Chrome OS will see the company enter the traditional PC space; the Chrome browser competes with Apple's Safari; and this fall, Google TV will be released and will compete with Apple TV.
In March The New York Times reported that Steve Jobs feels Google betrayed Apple by partnering with hardware manufacturers to make cell phones that resemble the iPhone. Jobs also allegedly let his feelings be known to employees at a company meeting in January.
"We did not enter the search business. They entered the phone business," Jobs reportedly said. "Make no mistake, Google wants to kill the iPhone. We won't let them."
The executive made similar comments on the record in early June, at The Wall Street Journal's All Things D conference, noting that his company wants to make better products than Google. He said that competing, however, doesn't mean you have to be rude.
"We didn't go into the search business," Jobs said of Google.
Despite animosity between Google and Apple, Jobs was spotted having coffee in public with Schmidt back in March. The two were seen talking at a cafe in Palo Alto, Calif.