It was the one that got away. Phil Mickelson came within a whisker of major championship history at Royal Troon last night as the 46-year-old set a blistering early pace in the 145th Open Championship.

The 2013 champion’s birdie putt from around 18-feet on the 18th hole burned the cup and stayed out as Mickelson signed for a superb course-record eight-under 63 to open up a commanding three stroke advantage over Patrick Reed and Martin Kaymer on a leaderboard peppered with his fellow Americans.

Had that putt dropped, Mickelson would have become the first player in the history of the major championships to shoot a 62 but the agonising late twist left the Californian wanting to “shed a tear” despite his position of authority on the standings.

“It was one of the best rounds that I've played,” he said. “I mean, nothing will match that final round at Muirfield (when he won the Open in 2013), but it was one of the best rounds I've ever played and I was able to take advantage of these conditions, and yet I want to shed a tear right now.

“That putt on 18 was an opportunity to do something historical. I knew it, and with a foot to go I thought I had done it. I saw that ball rolling right in the centre. I went to go get it, I had that surge of adrenaline that I had just shot 62, and then I had the heartbreak that I didn't and watched that ball lip out. It was, wow, that stings. It really stings to have a chance. It's such a rare opportunity to do something historic like that and. Had I just hit a weak flail-off and never had a chance and left it short, so be it. But this ball was hunting right in the centre and didn't go in. It was just heartbreaking even after such a great round.”

Mickelson finished third the last time the Open was held at Troon in 2004. Having always battled with the nuances of the links game, he maintains that performance then was a key part in his development even though it took almost a decade for it to reap the ultimate rewards when he captured the Claret Jug three years ago.

He added: “At Troon in 2004 is when it really clicked. After the first round I shot two-over, and I came back and shot three rounds in the 60s. That was my first real solid effort over here. It took me a while to break through and ultimately win it, but I did, and that's what matters."

While Mickelson surged to the head of affairs, Rory McIlroy had another say on the Olympic issue which had dominated the build up to the third major of the season.

The world No 4 began his challenge to recapture the Claret Jug he won in 2014 with a 69 before reaffirming his belief that golf in the Olympics simply does not rank high on his list of priorities.

McIlroy withdrew from the Games citing concerns over the Zika virus but in an honest yet withering assessment of the sport’s place in the Olympics earlier in the week, the four-time major winner admitted that he would not even watch the golf on the television, preferring to tune in to the “stuff that matters.”

Speaking after his opening round yesterday, McIlroy said: “I've thought about Olympics and golf for the last seven years and I decided it was time to stop dancing around the issue and actually tell everyone what I thought.

"Some people don't like it, I get that; it's my opinion and my opinion may be wrong, I may be wrong in a lot of people's minds but to me it's just how I feel. I don’t think anyone can blame me for being too honest, but at the same time it was seven years of trying to give the PC answer and finally I just cracked."

McIlroy, who donated his £515,000 first prize at May’s Irish Open to his own Foundation, had said that he didn’t get into golf to “grow the game”, a phrase which has been used to champion the sport’s inclusion in the Olympics.

"I think I would have elaborated a little bit on the grow-the-game comment,” McIlroy added. “Obviously I feel like I do my bit to grow the game. It's not as if I'm uninterested. I don't want to force golf on anyone, but I feel like golf is a great vehicle to instil values in kids. I'm an ambassador for the PGA Junior League, I do some stuff for the First Tee in the States and I feel like I've used my success in golf in a very positive way in the community.”