Carl Icahn is betting $100 million that ride-sharing startup Lyft Inc. can keep growing in a world increasingly dominated by its larger rival, Uber Technologies Inc.

The activist billionaire on Friday said he is backing Lyft because he considers its valuation of $2.5 billion a “tremendous bargain” compared with Uber, most recently valued by investors at $41 billion.

Mr. Icahn is now one of the most prominent supporters of San Francisco-based Lyft, the underdog in one of Silicon Valley’s most heated rivalries. In their race to sign up millions of passengers and secure a role in the future of urban transportation, Lyft and Uber have spent heavily to undercut each other’s prices, poach drivers and copy each others’ latest technological moves. Both also face regulatory challenges.

Coca-Cola versus Pepsi this is not. Lyft operates in 65 U.S. cities, compared with 300 world-wide for Uber. Lyft has 400 employees—less than 15% the staff at Uber—and has yet to prove the still-nascent business of car-hailing services can support a second player.

“There is room for two,” Mr. Icahn said in an interview.