The Hugh Jackman tale about machines in the boxing ring took in $16.3 million, which would make it the No. 1 movie for the second-straight weekend, according to studio estimates Sunday.
But "Real Steel" came in barely ahead of the remake "Footloose," which opened with $16.1 million.
The movies are close enough that they could switch rankings once final numbers are released Monday.
Studio estimates are based on actual business Friday and Saturday and projections for Sunday based on how well similar movies typically hold up.
An executive at Disney, which is distributing "Real Steel" for DreamWorks Pictures, said he expects his movie will come out on top because of strong family crowds during day-time shows Sunday.
"Absolutely," said Dave Hollis, Disney's head of distribution. "The way we've been playing, the families who've been coming and the kind of day-time business we've had on each of the weekend days so far, we have the expectation that it won't be terribly close. They're free to estimate as they will, but we expect to be No. 1."
Paramount, which released "Footloose," was tracking its movie's revenues slightly ahead of those for "Real Steel," said Don Harris, Paramount's head of distribution.
"Footloose" was doing especially strong business in the Midwest and South, and the studio had hopes that those rural crowds would turn out in big numbers Sunday, Harris said.
"It's close enough to be a dead heat at this point," Harris said. "If we get that middle of the country that seems to be preoccupied with high school football on Friday and college football on Saturday, then it bodes well not only for a big Sunday but for the legs of the movie."
Universal's horror update "The Thing," about Antarctic researchers stalked by a shape-shifting alien, opened at No. 3 with $8.7 million. Steve Martin, Jack Black and Owen Wilson's bird-watching comedy "The Big Year," released by 20th Century Fox, flopped at No. 9 with a $3.3 million opening.
"Real Steel" raised its domestic haul to $51.7 million. The movie also took in $23.3 million overseas to lift its international total to $56.6 million and its worldwide earnings to $108.3 million.
"Footloose" is a new take on the 1980s flick about a youth (Kenny Wormald) challenging a town's ban on dancing. The remake also features Dennis Quaid and former "Dancing with the Stars" contestant Julianne Hough.
It's rare that the top two movies flip-flop in the rankings after final numbers come out Monday.
Last summer, Universal's "Cowboys & Aliens" and Sony's "The Smurfs" were tied for No. 1 right to the dollar based on Sunday estimates. But "Cowboy's & Aliens" finished $800,000 ahead once Monday's final numbers were released.
"There have been a lot of close races this year," said Paul Dergarabedian, an analyst for box-office tracker Hollywood.com. "I don't think there have been as many breakout hits, so you have a lot of these films just kind of bunched up together."
Estimated ticket sales for Friday through Sunday at U.S. and Canadian theaters, according to Hollywood.com. Where available, latest international numbers are also included. Final domestic figures will be released Monday.
1. "Real Steel," $16.3 million ($23.3 million international).
2. "Footloose," $16.1 million.
3. "The Thing," $8.7 million ($1.5 million international).
4. "The Ides of March," $7.5 million.
5. "Dolphin Tale," $6.3 million.
6. "Moneyball," $5.5 million.
7. "50/50," $4.3 million.
8. "Courageous," $3.4 million.
9. "The Big Year," $3.3 million.
10. "The Lion King," $2.7 million ($5.2 million international).
Universal and Focus are owned by NBC Universal, a unit of Comcast Corp.; Sony, Columbia, Sony Screen Gems and Sony Pictures Classics are units of Sony Corp.; Paramount is owned by Viacom Inc.; Disney, Pixar and Marvel are owned by The Walt Disney Co.; Miramax is owned by Filmyard Holdings LLC; 20th Century Fox and Fox Searchlight are owned by News Corp.; Warner Bros. and New Line are units of Time Warner Inc.; MGM is owned by a group of former creditors including Highland Capital, Anchorage Advisors and Carl Icahn; Lionsgate is owned by Lions Gate Entertainment Corp.; IFC is owned by Rainbow Media Holdings, a subsidiary of Cablevision Systems Corp.; Rogue is owned by Relativity Media LLC.