May 8 (Reuters) - Lyft LYFT.O increased its stock buyback program to $750 million and posted a 14% rise in first-quarter revenue on Thursday, signaling steady demand for its ride-hailing services.

The company, which is expanding beyond major U.S. cities into smaller markets, said it intends to use $500 million of the authorization within the next 12 months. It disclosed its first share repurchase program in February, but did not specify a timeline.

Last week, activist investor Engine Capital urged Lyft to undertake a $750 million accelerated repurchase and said it wanted the company to consider strategic alternatives, including a sale.

The ride-hailing platform forecast second-quarter gross bookings and adjusted core profit largely in line with analysts' estimates.

Its first-quarter revenue of $1.45 billion, however, was slightly below analysts' average estimate of $1.47 billion, according to data compiled by LSEG.

The company posted adjusted core earnings of $106.5 million during the first quarter, above the estimate of $92.4 million.

Larger rival Uber UBER.N, with a global food and grocery delivery business, offered an upbeat second-quarter forecast on Wednesday, but attributed its lower-than-expected first-quarter revenue to sluggish U.S. travel demand.

U.S. spending on both lodging and tourism-related activity in March was down about 2.5%, according to Bank of America data, signaling souring consumer sentiment amid economic volatility.

With growth rates stagnating in major U.S. metropolitan areas, ride-hailing companies are increasingly focusing their expansion efforts on less densely populated cities with limited public transport options to capture new markets and drive growth.

Lyft is targeting smaller, car-dependent markets such as Indianapolis, where rides grew 37% in the first quarter.

The company expects gross bookings between $4.41 billion and $4.57 billion for the second quarter, compared with the estimate of $4.5 billion.

It forecast current-quarter adjusted earnings before interest, tax, depreciation and amortization at $115 million to $130 million.

(Reporting by Akash Sriram in Bengaluru; Editing by Shilpi Majumdar)

((Akash.Sriram@thomsonreuters.com; On X as @HoodieOnVeshti; +91-99017-77617;))