Phelps, 27, overtook Russian gymnast Larisa Latynina as the most decorated Olympian by helping the United States win 4x200m freestyle gold.
“It has been a pretty amazing career but we still have a few races left,” said the American.
Asked if his record would be broken, he responded: “Nothing’s untouchable.”
He added: “I’ve always said that anything is possible. I have put my mind on doing something that no-one had ever done before and there was nothing that was going to stand in my way.”
Phelps, who missed out on gold in the 200m butterfly final by 0.05secs earlier on Tuesday, thanked his team-mates who gave him a sizeable lead heading into the final relay leg.
“We’ve had a lot of history together they gave me a big lead,” he said. “I thanked them for helping me to this moment.”
Phelps will return to the pool on Wednesday for the 200m individual medley heats before competing in the 100m butterfly and 4x100m medley relay later in the week.
He began his quest for more medals by finishing fourth in the 400m individual medley on the opening day of action in the swimming pool.
“The very first day I was probably super uptight and trying to be super-serious,” he said. “Just the last couple of days, I’ve been laughing all of the time and joking and having fun.
“That’s what I said I wanted to do in the beginning and that’s what’ll I’ll do for the rest of the week.”