Trucking companies are competing to offer faster delivery as more shippers say they’re willing to pay extra for speedier service.

YRC Worldwide Inc., YRCW -4.35% one of the largest trucking companies in the U.S., said Monday it will start offering an “accelerated” service, which shaves a day or two off transit times. The new service is aimed at online retailers and other shippers that need to move goods fast, said YRC Freight President Darren Hawkins. Those customers will pay an average of 15% extra for faster service, he said.

YRC’s move is the latest salvo in an escalating rivalry between the largest companies in the $35.1 billion “less-than-truckload,” or LTL, industry. LTL carriers combine shipments from multiple customers in their trucks. Such companies have strategically-located distribution centers and use proprietary software to map out shipping routes that can serve thousands of shippers while minimizing the number empty trailers on the road.

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LTL companies are increasingly under pressure to speed up their delivery times as retailers looking to get goods quickly to online customers force their suppliers to produce and ship goods faster. Meanwhile, the trucking companies are also under pressure from rising labor costs and new regulations.

“It’s the Amazon Prime effect. Everybody believes that everything can be delivered in two days,” said Candace Holowicki, director of global transportation and logistics at TriMas Corp., which ships engineered components to manufacturers. The effect “moves farther and farther up the supply chain, nobody’s immune.”

Ms. Holowicki said she could consider YRC’s new service, but only if it shortens its delivery period by a minimum of two days.

“Before, you could tell a customer the standard delivery is two weeks, and they were fine with it. Now, that’s not acceptable,” she said.

YRC in particular operates in “more the economy market, a slower service than a lot of their competitors,” including FedEx Corp., XPO Logistics Inc., and Old Dominion Freight Line Inc., said Michael Scheid, analyst at SJ Consulting Group Inc. “They’re trying to speed up their service to better compete with those companies.”

Accelerated shipments in YRC’s network will take priority and be loaded onto trucks ahead of standard shipments. But they won’t be delivered at guaranteed times in the same way as its fastest “Time Critical” shipments, which are dispatched as fast as possible, or even by air, to make a delivery deadline.

“Every LTL carrier is dealing with how to respond to the growth in e-commerce. That’s at the top of all our lists,” Mr. Hawkins said. A broader portfolio of services and price points “allows us to do whatever the customer needs … so we can protect our margins.”

YRC is introducing its accelerated service just as one of its biggest rivals, XPO, is considering lower-cost services that would compete with YRC’s standard shipping rates. XPO, which entered the market through a $3 billion acquisition of LTL carrier Con-way last year, is suing YRC for allegedly poaching senior executives who took part in the research for that strategy, according to court documents.

YRC has denied the allegations in court filings, saying XPO has no proof of its allegations, and is using the lawsuit to suppress normal competition. A spokesman for XPO, which is also suing another LTL carrier for poaching, declined to comment on the legal proceedings.

Mr. Hawkins declined to comment on the case, but said YRC’s new service is not aimed at competing with any particular company, but rather “allows us to compete with a majority of the national carriers.”

Write to Loretta Chao at loretta.chao@wsj.com