FOXBORO — Weeks after signing a franchise record four-year, $104 million contract in free agency, Milton Williams ran sprints at the start of the Patriots’ offseason program.

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Toward the end, Williams pulled ahead of most of his surrounding teammates on the practice fields behind Gillette Stadium. Then he eyed the clock showing he was well ahead of the time to beat. He slowed down and cruised across the finish line.

Watching Williams run, Mike Vrabel got hot and chastised his star pass rusher for not sprinting to the end.

“He called me out and let me know, like, ‘Hey, you’re gonna be here, you need to set the standard,’” Williams said Tuesday at Gillette Stadium.

Vrabel’s message: “If you can make it faster, make it.”

It left an impression on Williams.

“Every rep since then, I just try to make sure I’m the first one back,” he said. “I feel like that’s going to help me, push me to where I want to be. The guys that are running with me, that’s going to push them even harder.”

Williams, 26, is the rock upon which Vrabel is rebuilding the Patriots’ defense and — to some extent — their program. Before Williams can create pressure on Sundays this fall, he’s been a regular at the offseason program that just entered its sixth week. His presence, as the highest-paid player in franchise history by average annual value, is notable in that it reinforces Vrabel’s culture. By contrast, after the Patriots signed Pro Bowl edge rusher Matthew Judon to a rich four-year deal back in 2021, he did not attend voluntary team activities that spring.

Last season, Williams was the best player in the Super Bowl and NFC Championship Game, totaling eight pressures, two sacks, a forced fumble and a couple pass deflections for the Eagles. He is hoping to form a similarly ferocious defensive line with Christian Barmore, who has also been a regular in Foxboro. Williams said the two have been competing to see who can show up first at the facility in the morning.

As for Vrabel’s demanding style during a time of voluntary workouts and meetings, Williams said it suits him.

“I like that. I don’t mind. I don’t think I’m bigger than the next person. I don’t mind being called out,” he said. “Him calling me out is just going to help the other guys. We ain’t got no excuses for nobody to not be giving their all.”