"If I could, I would take this ... ball and shove it down your ... throat," Williams told a line judge, according to a tennis official who watched a replay Saturday night.
The official also said Williams used the word "kill." The official declined to be identified because the tape was still being reviewed. Williams denied using that word on court.
The $10,000 fine — not quite 3 percent of the $350,000 in prize money Williams earned by reaching the semifinals — is the maximum on-site penalty that can be issued for unsportsmanlike conduct at a Grand Slam tournament.
"The average individual would look at that and say, 'A $10,000 fine for what she did? What are you guys, crazy?' The answer is: the process isn't over," tournament director Jim Curley said in an interview with The Associated Press.
Bill Babcock, the top administrator for Grand Slam tournaments, will review what happened Saturday night, when Williams yelled at a linesperson who called a foot fault with the defending champion two points away from losing to Kim Clijsters in the semifinals.
If Babcock determines Williams committed a "major offense," the rules allow for a fine as high as all of a player's prize money from the tournament — and a suspension, although Curley did not mention that as a possibility.
Williams also was docked $500 for smashing her racket after the first set of the match. Because she was issued a warning then, her later actions resulted in the loss of a point.
The foot fault resulted in a double-fault, which moved Clijsters one point from victory. Williams then was penalized a point for her outburst; because it happened to come on match point, it ended the semifinal with Clijsters ahead 6-4, 7-5.
Clijsters won the final Sunday by beating Caroline Wozniacki 7-5, 6-3.
Babcock did not immediately respond to requests for comment. But Curley said the inquiry probably would include reviewing TV footage, checking additional audio feeds from courtside microphones and interviewing Williams, the linesperson, the chair umpire and possibly spectators.
"What she did was unacceptable. It's unacceptable behavior under any circumstances. When you're on the court, and you are waving your racket toward a linesperson and using profanity, it's just simply unacceptable," Curley told the AP. "When you look at the tape, it's pretty clear that the way she approached the linesperson, with her racket and in that manner, it was a threatening manner. It certainly was."
The names of linespersons are not disclosed as a matter of practice at the tournament.
He also said the tournament considered — and decided against — preventing Williams and her older sister Venus from participating in the women's doubles final Monday. Venus put in some work on a U.S. Open practice court Sunday; Serena wasn't with her.
Serena Williams made an onstage appearance at the MTV Video Music Awards in New York on Sunday night, where there was no mention of what happened 24 hours earlier. She did release a statement through a public relations firm, acknowledging that "in the heat of battle I let my passion and emotion get the better of me and as a result handled the situation poorly."
She did not apologize for the outburst, which made the "most viewed" page of YouTube with four different versions that totaled more than half a million clicks as of Sunday night.
After what may be recalled as the most significant foot fault in tennis history, Williams paused, retrieved a ball to serve again and then stopped. She stepped toward the official, screaming, cursing and shaking the ball at her.
Fans began booing and whistling, making it difficult to hear the entirety of what Williams said — and she refused to discuss specifics afterward at a news conference. An AP reporter — provided access to replays — could not verify Williams used the word "kill."
When Williams turned her back, the line judge went over to the chair umpire to report what was going on. The line judge then returned to her seat, and Williams pointed and began walking toward her. The line judge then headed back to the chair umpire's stand. By now, tournament referee Brian Earley was on the court, too.
Earley could be heard asking the linesperson what Williams said.
That's when Williams walked over and said to the line judge: "Are you scared? Because I said I would hit you? I'm sorry, but there's a lot of people who've said way worse."
Earley again asked the linesperson what Williams said. Whatever the linesperson said, her reply seemed to startle Williams, who said: "I didn't say I would kill you. Are you serious? Are you serious? I didn't say that." The line judge then said, "Yes."
The episode dominated conversation at the U.S. Open on Sunday, including whether the line judge should have made the call in the first place. Foot faults are rarely called at this level, particularly in possibly the final moments of such a significant match.
"In my opinion, you can't call a foot fault there. Just out of question. Can't do it. It was so close. Not as if it was an obvious foot fault — it was minuscule," TV commentator John McEnroe said. "I've seen Serena come back from that position a dozen times against top-flight opponents. The match was not over."
The chairman and CEO of the women's tennis tour, Stacey Allaster, issued a statement calling Williams' conduct "inappropriate and unprofessional."
"No matter what the circumstances, no player should be allowed to engage in such behavior without suffering consequences," Allaster said. "I have spoken with the USTA about this matter and I agree with the action they have taken."