Kofstad was 6-under on the back nine, with birdies on all three par 3s.
Green played bogey-free golf Thursday and Wood's round included four birdies, a bogey and an eagle at the par-4, 477-yard 15th home.
Kofstad birdied his first two holes at the Celtic Manor Resort in southeastern Wales but had a bogey at the ninth hole after six straight pars to make the turn on 1-under.
He opened his second nine with a birdie and added another at the 13th. After giving back a stroke at 14, Kofstad ran off three consecutive birdies -- making a long putt on 17 -- and had a bunker shot go in for eagle at 18.