Sony's board and management unanimously concluded that retaining the chips business, which includes imaging sensors,
was "the best strategy for enhancing Sony's corporate value over the long term", the company said in a letter to shareholders.
The rejection comes just weeks after Sony sold its 5% stake in Olympus Corp back to the Japanese medical equipment maker, a move also called for by Loeb, one of the world's highest-profile activist investors.
Sony said staying within the group would help the chips business enhance its competitiveness as it aimed to combine sensors with artificial intelligence for use in autonomous driving, games and advanced medicine.
Third Point did not immediately respond to a request for comment outside business hours.
Sony is the world's top supplier of image sensors for smartphone cameras, providing them to most major global smartphone makers including Apple Inc and Huawei Technologies [HWT.UL].
Smartphone makers' adoption of multiple-lens cameras and large-size image sensors drove Sony to a record April-June operating profit.
Loeb has also called on Sony to sell off stakes in Sony Financial, Spotify and other non-core assets, to position itself as a leading global entertainment company, blaming Sony's valuation discount on portfolio complexity.
Sony rejected the sale of Sony Financial, saying it believed "at this time" that retaining the holding company for insurance and banking units would also enhance the corporate value of Sony.
Shares of Sony have risen 36% since early April, when Reuters reported that Loeb was building a stake in the company to push for change. The effort marks the second time in six years that Loeb has targeted Sony.
(Reporting by Makiko Yamazaki and Junko Fujita; Editing by Louise Heavens & Kim Coghill)
By Makiko Yamazaki