The team are third overall ahead of the cross-country after the 43-year-old scored a personal best dressage score of 44.10 penalties on his horse Lionheart.
And the world No.1 is expecting his young mount to show his ability over the next few days as Great Britain look to challenge leaders Germany.
“Hopefully he’s going to come into his own the next couple of days and that’s why he’s here,” said Fox-Pitt.
“At ten-years-old, Lionheart is a lot younger than some of the other horses, and this is his first championship.
“He’s in the toughest company in the world and not far off the lead, so we’re certainly hoping things go our way tomorrow.”
Great Britain are just 7.9 penalties shy of leaders Germany, and 4.9 penalties behind second-placed Australia.
And Fox-Pitt – who is competing in his fourth Games – also praised the performance of his team-mates’ horses which have impressed team manager Yogi Breisner.
He said: “All the horses have gone very well and Yogi is thrilled. They’ve all done as good a test as we could have hoped and you can’t expect for more.
“I know that the next couple of days are going to be demanding and I hope we’re all going to be able to answer the questions.”