Furyk and Martin, among half the field unable to finish the round on Friday before bad weather struck, took advantage of favorable scoring conditions at Harbour Town on Hilton Head Island.
With the course softened by torrential rain Friday and overnight and with the wind down, 2010 champion Furyk carded a bogey-free five-under-par 66, while Martin shot a 68.
They matched Choi, who finished his round on Friday, at five-under 137, two shots ahead of a large group including joint first round pacesetter Matt Kuchar and England's Luke Donald (69).
Kuchar certainly benefitted from the delay. He ran up two early double-bogeys in brutal conditions before play was halted on Friday, but was much more assured when he resumed on the seventh hole Saturday, battling his way to a reasonable 73.
"I'm amazed how well the course handled all the rain," 2003 U.S. Open champion Furyk said after recording the best second round score.
Martin was grateful for the Saturday weather reprieve.
"I played four-and-a-half holes yesterday and it was windy and rainy but still pretty firm," the South Carolina native told Golf Channel.
"This morning the wind died down a little bit but (the course) definitely softened up.
"I'm sure I'll be worn out at the end of the day but it's nice to have a few holes under my belt."
Seventy-eight players made the cut, which fell at four-over 146.
Veterans Tom Watson, Nick Faldo and Davis Love all missed the cut, allowing Faldo to segue into the TV commentary box for the final two rounds.
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