Rickie Fowler has a one-shot lead going into the final two rounds of the U.S. Open ©Getty Images

Rickie Fowler has taken the outright lead after the second round of the U.S. Open as he continues his quest for a long-awaited first major title.

After posting the lowest score in the tournament's history along with fellow Californian native Xander Schauffele yesterday, Fowler hit the front on his own with another strong round at the Los Angeles Country Club.

It was not as spectacular as his historic eight-under-par 62 24 hours earlier, but Fowler hit more birdies than bogeys to put himself in the lead.

Fowler made eight birdies, four pars and six bogeys to score a two-under-par 68 to top the leaderboard at the halfway stage on 10 under.

"It’s not that easy out there," said Fowler, who has finished in the top three in all four majors but never been crowned champion.

"Yes, I’ve made a lot of birdies, and that is doable out there.

"It’s still a very hard test.

"You hit fairways and hit greens, yes, you can score well, but you get out of position and it’s going to eat you up."

Unlike Fowler, Schauffele was unable to back up his stunning first-round display to maintain the lead as he slipped to third on eight under after finishing on even par for the day.

The reigning Olympic champion is joined in third spot by Northern Ireland’s Rory McIlroy who is aiming to win his first major since capturing the 2014 PGA Championship crown.

McIlroy finished the round with a three-under-par 67 to leave him just two shots behind Fowler.

"I started thinking about winning this thing when I came here on Monday," said McIlroy.

"No one wants to win another major more than I do.

"The desire is obviously there."

American Wyndham Clark also scored a three-under-par round to move into second position as he looks to put pressure on Fowler.

Harris English of the US is in fifth on seven under, while another American in Dustin Johnson is tied sixth with Australia’s Min Woo Lee on six under.

"Everything that you could do wrong I did wrong," said Johnson.

"It happens sometimes, but [I] just battled back and played a really good round of golf."

One of the highlights of the day was a hole-in-one on the 15th by defending champion Matt Fitzpatrick of England.

"As soon as I hit it I thought that it got a good chance of going close anyway," said Fitzpatrick who is tied 39th on one over.

"Dead centre.

"My hand was a bit sore afterwards, I'll be honest, after all the high fiving."