Apple's rising shares lifted the iPhone maker's market cap above that of Microsoft.
Apple's stock recently stood nearly 3% higher.
The gains followed a more-than 7% jump yesterday, powered by optimism about its new AI offerings, that left its shares at a record high.
Apple's market cap was recently at $3.25 trillion, making it the most-valuable U.S. company.
It was the first time since January that Apple has had a higher market value than Microsoft.
