The two-time Sprint Cup champion also hit Busch with his fist inside a NASCAR hauler, sources close to the situation confirmed on Saturday.
The second incident occurred while the drivers discussed the first incident with series director John Darby and vice president of competition Robin Pemberton.
Officials from NASCAR, Joe Gibbs Racing and Penske Racing would neither confirm nor deny the punch occurred, saying what happens in the hauler stays in the hauler.
Darby, however, said a Saturday morning meeting, which was called to give all parties time to cool off, was less "hostile."
"Partially, I wanted to make sure that in the heat of everything last night our message was delivered very clearly to both competitors," he said. "So we let them go back to the buses and sleep on it overnight."
The message? That both drivers should go out of their way to avoid each other during Saturday's two practice sessions for Saturday night's Budweiser Shootout and the Daytona 500 on Feb. 17.
"This morning, in a less hostile atmosphere without all the screaming and hollering and us banging our fist on the table, we sat back down and went through the whole conversation to make sure they know what we expect," Darby said.
Asked if Stewart punched Busch, Darby replied, "There's a reason why we do have an office with a door on it."
Stewart, who was accompanied by team owner Joe Gibbs on Saturday, issued a statement after the second meeting. It did not address whether he took a swing at Busch.
"I'm not mad at him about what happened on the racetrack at all," Stewart said. "What happened, happened. We can't fix it. We can't change it. The best thing to do is go on and move forward and not let this linger between the two of us.
"We've met with NASCAR twice now, and we're both past it, and we're hoping the media will respect that fact, too, and let us move on from it."
When asked about the incident after Saturday's Bud Shootout, Stewart said what happens behind closed doors stays behind closed doors.
No fines were issued, although NASCAR officials said there could be some next week. Gibbs, who has made more than his fair share of trips with Stewart to the principal's office of NASCAR, jokingly said this wasn't why he retired as head coach of the Washington Redskins last month to return to racing.
"I want to come back and win," said Gibbs, who has three Cup titles, two with Stewart, since 2000. "We'll see what happens. We haven't gotten to the race, yet."
Stewart and Busch, two of NASCAR's most controversial characters, got into a sheet-metal exchange on pit road after an on-track incident that wrecked both of their cars halfway through Friday night's practice.
The confrontation began when Stewart tapped Busch from behind, forcing Busch into the wall. Busch felt Stewart caused the accident and retaliated by bumping Stewart's car with his on the way to the pit-road entrance.
Stewart felt Busch caused the accident by blocking.
"That was a racing accident, totally," NASCAR spokesman Jim Hunter said. "We looked at it from a bunch of different angles. The two drivers are the only people who really know what happened. When you look at the replays on television it is very inconclusive.
"What they emphasized in the meeting was you two guys better give each other a lot of space."
Both drivers immediately were summoned to the NASCAR hauler to meet with Darby and Pemberton. The only words spoken by either driver -- both left through a side door without commenting -- came from Busch before entering the hauler.
"It's a great way to start off 2008," he said, clapping his hands together.
Neither driver spoke again immediately after Saturday's meeting as they went to their cars for the first practice. Busch later said he was confused why such an incident would happen in practice.
"Tony and I are competitors, we always have been and we're going to be just fine," he said.
Gibbs said the incident was "just part of the racing world."
"It's just something you deal with," he said. "Anytime you're in sports with the competitive spirit everybody has you run the risk of somebody getting sideways, in more ways than one."
NASCAR will be watching to make sure the drivers don't get sideways again anytime soon.
"We're going to continue to think about it and talk about it and handle it just like any other penalty," Hunter said. "If there are [penalties], we'll talk about them Monday or Tuesday."
This wasn't the first time the two have clashed. Busch was fined $100,000 and docked 100 championship points in June after sending Stewart into a barrier at Dover and nearly hitting a member of Stewart's crew on pit road.
He also was parked for the remainder of the race.
"Both of them are so competitive," said Hunter, noting any fine likely would be less than what Busch received because there were no crew members on pit road. "Both of them are hardheaded. And both of them want to win. There you have it."
Hunter said what happened showed the fine line between letting drivers be
themselves as NASCAR chairman Brian France stated as a goal for 2008 and crossing the line where safety becomes an issue.
"I don't mean we want things like that to happen on the racetrack," he said. "But we like our guys to be emotional. If they're mad, vent it. Our responsibility is to make sure when they're in those race cars they don't lose their heads for safety reasons."
David Newton covers NASCAR for ESPN.com. He can be reached at email@example.com.