Park, ranked No. 1 in the world and the winner of five tournaments this year, shot a 4-under-par 68 at the Sebonack Golf Club and posted a 36-hole total of 9-under 135.
I.K. Kim, who has finished in the Top 10 in this tournament four of the last five years, was alone in second at 137 following a round of 69.
Park was able to finish shortly before USGA officials decided the fog that rolled across Long Island was too thick to allow play to continue. There were 41 players on the course when the suspension came.
The second round will resume at 8 a.m. EDT Saturday and the third round will begin shortly after all the players have finished 36 holes.
Lizette Salas was in third place, a distant five shots behind Park after firing an even-par 72 that put her at 4-under 140. Jodi Ewart Shadoff was also at 4-under with three holes remaining.
Angela Stanford and Jessica Korda shared fifth place at 141.
First-round leader Ha-Neul Kim, who earned an invitation to the tournament by finishing first on the Korean Tour's money list last year, stumbled to a 77 and finished the day in a tie for ninth place.
Although the cut will not be made until Saturday, it appeared it would take a score of 6-over 150 to play the final two rounds. Among those certain to miss out will be Michelle Wie, who was 11-over with one hole to play.
Park won the U.S. Women's Open five years ago and among her victories this season have been the Kraft Nabisco Championship and the LPGA Championship -- both major titles.
Babe Zaharias has been the only player to win three majors in the same year on the LPGA Tour, a feat she pulled off in 1950.
Swim Week Miami Beach 2014 [PHOTOS]