Mickelson and Koepka are among a group of 11 players on four under par after rounds of 66 at TPC Southwind.

Power, who went to university in Tennessee, had six birdies and one bogey in his 65.

World number two Dustin Johnson is just a shot further adrift after a round of 67, which included a chip-in birdie.

Johnson holed a wedge from the edge of a water hazard on the par-four 12th after removing his right shoe and sock to take his stance in muddy water.

"I actually didn't hit it very well and got lucky and it went in the hole," he said.

Mickelson will again try to complete the career Grand Slam at Shinecock Hills next week after six runners-up finishes at the US Open.

The 47-year-old, who won The Open in 2013 to add to his PGA Championship and three Masters titles, said: "I had a nice simple round going and then I missed the last four fairways.

"I finished the round off, even though I didn't quite have it there at the end, I was able to gather myself and control my thoughts a little bit better."

Koepka, who has missed a lot of this season with a wrist injury, conceded "I didn't play well at all," adding he was "all over the place".

"I'm a good putter. I just need to figure out everything else."