text: Fleetwood shot a four-under-par 68 to keep pace with fellow overnight leader Brooks Koepka at Erin Hills, while Harman carded a 67 to lead on 12 under.
  Paul Casey, who also started on seven under, fell away with a three-over 75.
  Justin Thomas is tied for second after becoming the first man to shoot a nine-under-par round at the US Open and the fifth 63 in its 117-year history.
  There had been four other 63s in US Open history before this week. Jonny Miller hit the first on the par-71 Oakmont in 1973, while Jack Nicklaus and Tom Weiskopf's efforts came on the par-70 Baltusrol in 1980.
  Fiji's Vijay Singh also recorded a seven-under 63, at Olympia Fields in 2003.
  The US Open tournament organisers have historically prided themselves on trying to make the winning score as close to level par as possible.
  However, heavy overnight rain dumped an inch of water on the course and that undoubtedly helped low scoring with players able to take advantage of receptive greens and attack the holes.
  Thomas opened his round with two birdies before dropping a shot on the fourth. Four more birdies followed on the front nine before another bogey on the 10th looked to have put paid to his chances of breaking Miller's 44-year-old record.
  But after three birdies in six holes, he eagled the 667-yard par-five 18th, hitting his second shot to eight feet from 300 yards and rolling in the downhill putt.
  Southport's Fleetwood, who finished tied for 27th on his only other US Open appearance in 2015, appeared to be heading towards his second bogey-free round of the tournament after laying up with his second shot on the par-five 18th.
  However, he left his chip to the green short and then putted through the green and off it with his fourth shot. A sublime chip to three feet allowed him to escape with just his third bogey of the week.
  "That was the best shot I hit all day," Fleetwood told BBC Sport.
  "I hadn't been out of position all day and suddenly I was staring double bogey in the face.
  "Bad shots make bogeys and 18 was a good example. I could still have been there now, hitting the ball over the green. But I hit the perfect shot and I was made up when I got on the green.
  "Three days down and so far so good."
  Fellow Englishman Casey was one of the four overnight leaders but he fared the worst, posting a triple bogey for the second day running as he dropped out of contention.
  His downfall began with an errant second shot on the par-four third into deep rough. That led to a seven and a further shot went on the next hole.
  On Friday, the 39-year-old responded with a run of five successive birdies but he was unable to replicate that on Saturday, as he ended the round on four under par.
  Home players occupy 12 of the top 16 places on the leaderboard and with six shots separating them, any one could still win on Sunday.
  None of the dozen have won a major, and neither have the four non-Americans (Fleetwood, Kim Si-woo, Bernd Wiesberger and Hideki Matsuyama).
  Harman, who is bidding to become the first left-hander to win the US Open, knocked in six birdies.
  The 30-year-old, who won the Wells Fargo tournament last month, said: "I've been striking the ball so well and giving myself chances so I'll just try to keep doing what I've been doing.
  "I'll definitely think about the mindset I had in winning Wells Fargo a few weeks ago."
  Big-hitting Koepka, who averaged 320 yards with his driver on Saturday, had five birdies in his four-under round.
  Rickie Fowler had a run of three successive birdies from the 14th as the leader from the first round shot a four-under 68 to get to 10 under and just two off the lead.
  Patrick Reed's seven-under 65 featured eight birdies and one bogey as he improved to eight under.
  He said he felt like he "hit the ball better" in Friday's second round, despite taking 10 fewer strokes on Saturday.
  Reed explained: "I was really seeing the lines and had the speed. And most of my birdie putts were uphill and I could attack. On Friday it was the opposite."
  Russell Henley (67) and Charley Hoffman (68) are all in a group four off the lead on eight under.
  However, not all Americans fared well. Jordan Spieth, the 2015 champion, started the day level par and was still on that mark after a couple of birdies cancelled out two bogeys in his opening 11 holes.
  Two more bogeys followed though and a double-bogey on the par-five 18th saw him finish four-over after a 76.
  "It's been an off-week for me with the putting," said the former world number one. "I've been striking the ball well.
  "It's just been trying to figure it out on and around the greens. And I feel like once the can gets open, I'll start pouring them in."
  Germany's Martin Kaymer, winner in 2014, took 41 shots to complete the front nine and although he picked up two birdies on the back nine, his three-over 75 saw him drop back to level par.
  And two-time winner Ernie Els, who was two under after round one, dropped five shots in his opening six holes on Saturday. The South African rallied with an eagle two on the par-four 15th but had a triple-bogey seven on the 17th to drop to five over after a 79.
  England's Eddie Pepperell, 26, had five birdies and two bogeys in his three-under-par 69 to get to four under and remain in with a chance.
  After dropping three shots in his opening six holes, Matt Fitzpatrick holed five birdies in eight holes to post a two-under 70 to climb to three under.
  Fellow Englishman Andrew Johnston mixed three birdies with four bogeys as he slipped back to one under with a 73.
  And Scotland's Martin Laird is putting together a solid tournament with nine birdies and nine bogeys in his opening three rounds.
  However, it looks like Lee Westwood's wait to win a major will go on to The Open in July. The Englishman was three under after round one, but he followed Friday's 75 with another 75 today to drop to three over.
  More to follow.
target: England's Tommy Fleetwood is one shot off Brian Harman's lead going into Sunday's final round of the US Open.