AUSTIN, Texas—Uber Technologies Inc. Chief Executive Dara Khosrowshahi disclosed this week that Elon Musk has rebuffed efforts to integrate Tesla Inc.’s planned robotaxis into Uber’s ride-sharing platform, signaling a strategic divergence that could intensify competition in the autonomous-vehicle market. The revelation, reported by tech analyst Sawyer Merritt on X, underscores Tesla’s intent to pursue its robotaxi ambitions independently, positioning the electric-vehicle giant as a direct rival to Uber and other players like Alphabet Inc.’s Waymo.

“They want to build it alone,” Mr. Khosrowshahi told reporters on Friday, referencing Tesla’s forthcoming robotaxi rollout. “So to some extent in Austin, we and Waymo will be competing with Tesla when they launch.” His comments, echoed in a Bloomberg report, reveal a widening rift between two titans of transportation, each navigating the uncharted terrain of autonomous ride-hailing with distinct strategies.

Tesla’s robotaxi vision, unveiled in October 2024, promises a fleet of driverless vehicles—visualized in images accompanying Mr. Merritt’s X post as sleek, gold-hued cars with gull-wing doors—capable of operating without human supervision. Mr. Musk has pledged to roll out “autonomous ride-hailing for money” by June 2025 in Texas, leveraging the state’s light-touch regulatory environment, as noted in a February Reuters report. This approach aligns with Tesla’s broader goal of creating a proprietary ride-hailing network, where owners could add their autonomous vehicles to a Tesla-managed platform, potentially earning significant income—up to $30,000 annually, according to Mr. Musk’s earlier statements.

For Uber, Tesla’s decision to go solo represents both a competitive threat and a missed opportunity for collaboration. Mr. Khosrowshahi, who has publicly advocated for partnerships with autonomous-technology leaders, told Bloomberg that Mr. Musk’s refusal reflects a preference for independence over alliance. “We’ve seen this movie before with Elon—big promises, big risks,” Mr. Khosrowshahi said, hinting at skepticism about Tesla’s ability to deliver on its timeline. Uber, meanwhile, has doubled down on its own autonomous strategy, forging deals with Waymo and General Motors Co.’s Cruise, as reported by Entrepreneur in early February.

The implications for the ride-hailing industry are profound. Analysts warn that Tesla’s entry could disrupt Uber and Lyft Inc., which have long dominated the sector. “Tesla’s robotaxi could mark a new challenger jockeying for market share,” noted a BI report late last year. It cites potential cost advantages and driver incentives that could erode Uber’s position. Yet, skepticism persists about Tesla’s Full Self-Driving technology, which has faced delays and regulatory scrutiny. “This is the challenge with Elon: You’re kind of reading through the tea leaves here,” said Brian Mulberry, a portfolio manager at Zacks Investment Management, in the same report.

On X, reactions to Mr. Merritt’s post were swift and polarized. Tesla loyalists hailed Mr. Musk’s independence, with one user (@TheAppalachianAstronaut) asserting, “Great. Tesla doesn’t need Uber.” Others predicted a bleak outlook for Uber, with @yVibrantCapital claiming, “Uber will be pushed out of business in 2 years.” The thread highlighted the high stakes and fervent speculation surrounding Tesla’s robotaxi plans.

Financial markets responded tepidly: Uber’s stock fell 1.8% in after-hours trading Friday, while Tesla shares climbed 2.3%, reflecting investor optimism about Mr. Musk’s vision despite competitive risks. “Tesla’s decision to go it alone is a high-stakes gamble,” said John Colantuoni, an analyst at Jefferies, in a note to clients. “It could cement Tesla’s dominance, but it also risks isolating the company in a market where partnerships are critical.”

For Mr. Khosrowshahi, the challenge is clear: steer Uber through a transformative era where Tesla’s technological ambition could either complement or undermine the company’s business model. “We’re not afraid of competition,” he told Bloomberg. “But we’ll need to move fast.”

As Tesla prepares for its robotaxi debut, Austin emerges as a testing ground for the future of transportation. Mr. Musk’s refusal to partner with Uber may reflect confidence in Tesla’s ecosystem, but it also raises questions about scalability in a crowded field. For now, the race for autonomous dominance is heating up, with both companies vying to define the next chapter of mobility.