SAN FRANCISCO — For years, Uber and Lyft put off going public. Now, they are speeding up.

Faced with a volatile stock market and the prospect of an economic downturn next year, the ride-hailing services have moved more urgently toward an initial public offering, said four people with knowledge of the companies’ plans, who were not authorized to speak publicly.

Lyft originally aimed to list its shares toward the middle of 2019, but it began moving more quickly after the recent stock market sell-off and because of a desire to go public before Uber, said two of the people. On Thursday, the company, which was most recently valued at $15 billion, announced it had filed confidentially for an I.P.O.

Uber has also hastened its I.P.O. clock. The company had once said it was looking to the fall of 2019 to go public, but has pushed that timing up because of concerns that a recession might be coming, said two people familiar with the plans. Uber could now go public as soon as next April, they said. Investment banks have told the company it could be worth as much as $120 billion in an I.P.O.