SpaceX shares held steady in premarket trading on Thursday, after the stock's recent rally showed signs of cooling following a record-breaking IPO last week.

Elon Musk's space and AI company saw its stock surge more than 40% after its historic debut last week, which offered shares at a set price of $135.

Investor bullishness showed signs of waning on Wednesday, however, as shares sank 5%. The stock was last 0.3% higher in premarket trading.

SpaceX immediately became one of the world's most valuable companies after listing, with its market cap surpassing Amazon and — briefly — Microsoft. Its valuation sat just below Amazon at $2.52 trillion at market close on Wednesday.

The rocket maker announced Wednesday that it's adding Musk's longtime friend and ally, Roelof Botha to the board.

Botha will serve as an independent director and a member of the company's audit committee, starting immediately. Botha becomes the eighth board member at SpaceX, where Musk serves as chairman, in addition to his roles as CEO and technology chief.

Musk ​controls more ⁠than 82% of voting rights at SpaceX and owns shares in the company worth over $1 trillion. The governance model gives outside shareholders little ability to exert influence.

Posting on X on Sunday, Musk said that the company "might be able to reach approximately" $1 trillion revenue in 2030.

— CNBC's Lora Kolodny helped contribute to this report.