The Swede, already the LPGA Tour record holder with five straight wins in this event, posted a 6-under 66 to finish 36 holes tied for third place at 7-under-par 137.
Sorenstam trails Japan LPGA member Momoko Ueda by two at Kashikojima Country Club in Shima. Ueda fired an 8-under-par 64 and is through two rounds at 9-under-par 135.
Sorenstam played in the first group out off the first tee on Saturday and flew out of the gate with a pair of birdies at her first two holes. She added back-to-back birdies at seven and eight to make her presence known on the leaderboard.
On the second nine, the Swede birdied the par-4 12th hole to reach 6 under par. Sorenstam birdied the par-3 17th to get within two shots of more LPGA Tour history.
Nabisco Championship winner Karrie Webb shot a 5-under 67 and is alone in second place at minus-8.
Sorenstam was joined in third by overnight leader Rachel Hetherington (72), Yun-Hee Ku (65), Jeong Eun Lee (65), Ai Miyazato (68), Aree Song (68) and Brittany Lang (69).
As Sorenstam got off to a great start in Saturday's second, Ueda in the group behind got off to an even better start.
She birdied the second and third holes, then collected back-to-back birdies from the sixth to get to reach 5 under par for the championship. Ueda recorded a birdie at the par-4 ninth to make the turn in 5-under 31.
Ueda birdied the par-5 13th to get into a share of the lead at minus-7. She birdied the 15th, a hole she bogeyed on Friday, then birdied the closing hole to take the 36-hole lead.
Ueda is currently 59th in the Rolex Rankings, but has yet to win on the Japan LPGA. Her best finish this season on that circuit was a tie for third place.
Webb, like most near the top of the leaderboard, did her damage on the front side. She birdied the first two for the second time in as many days, then tallied birdies at five and seven.
Webb only managed one birdie on the second side, a four at the par-5 13th, but she is certainly within striking distance of her fifth LPGA Tour title this year.
Maria Hjorth (68), Shinobu Moromizato (68), Nancy Scranton (69) and Mitsuko Kawasaki (70) are knotted in 10th place at 6-under-par 138.