Oracle's shares rose Thursday, adding to a record run in the previous session and lifting stocks across the tech sector, as the company inches closer to the coveted trillion-dollar club on soaring gains from its AI cloud business.

The enterprise software maker's remarkable rise, fueled by a wave of multi-billion-dollar cloud deals, puts the spotlight on the scramble for computing power from companies that are pouring billions to become leaders in the AI race.

The stock's gains also put Oracle co-founder Larry Ellison on course to beat Elon Musk as the world's richest man.

"Oracle lit a fire under the rekindled AI trade," said Richard Hunter, head of markets at Interactive Investor, adding that the company's billion-dollar demand outlook has triggered a "ripple effect" for AI-related stocks.

The Wall Street Journal also reported on Wednesday that OpenAI has signed a $300 billion deal with Oracle for computing power, among the biggest in history, likely accounting for the bulk of the new revenue Oracle outlined on Tuesday.

Oracle's shares were last up 2% in premarket trading after climbing as much as 35.9% on Wednesday, lifting the company's market capitalization to a record $933 billion, as of last close.

Co-founder Ellison saw his net worth soar by nearly $100 billion to $392.6 billion, largely driven by his 41% stake in Oracle, compared with Tesla CEO Musk's $439.9 billion fortune that still tops Forbes' global wealth rankings.

Shares of Nvidia and Broadcom, which supply semiconductors used in data centers, were also marginally up, extending gains from the previous session.

Peers in Asia also surged.

Oracle's shares were trading at a premium compared to its cloud services peers. Their 12-month forward price-to-earnings multiple was 45.3, compared to Amazon's 31.3 and Microsoft's 31.