Their warning comes after Moscow on Tuesday refused to rule out deploying its nuclear arsenal, saying it could be used in the Ukraine war if Russia faced an "existential threat".
Japanese leader Fumio Kishida and ambassador Rahm Emanuel visited a peace memorial park and museum, where the US diplomat called Russia's position "unconscionable".
Around 140,000 people died when Hiroshima was bombed in 1945, a toll that includes those who survived the explosion but died afterwards from radiation exposure.
Three days later Washington dropped a plutonium bomb on the Japanese port city of Nagasaki, killing about 74,000 people and leading to the end of World War II.
The United States remains the only country ever to have used nuclear weapons in conflict.
Emanuel issued a statement condemning Moscow's position.
"The history of Hiroshima teaches us that it is unconscionable for any nation to make such a threat," he said.
"We live in unprecedented times as Russia threatens the use of nuclear weapons, something that was once unthinkable, even unspeakable."
Kishida said "the horrors of nuclear weapons must never be repeated".
Days after Russian troops invaded Ukraine last month, President Vladimir Putin announced he had placed Moscow's strategic nuclear forces on high alert, in a move that sparked global alarm.
"We have a concept of domestic security, and it's public. You can read all the reasons for nuclear arms to be used," Kremlin spokesman Dmitry Peskov told CNN Tuesday.
"So if it is an existential threat for our country, then it can be used in accordance with our concept."
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