"I expressed our deepest regret about this matter and assured the prime minister we were giving the highest priority to it," Mr Prescott told the BBC.
The consignment from British Nuclear Fuel's Sellafield reprocessing plant in Cumbria was shipped to Japan last October - but the company has subsequently revealed data was falsified, casting doubts on its safety.
Tokyo is demanding that BNFL pays for the mixed plutonium and uranium oxide (Mox) fuel to be shipped back to Britain.
At the same time, Japan and Germany have suspended all Mox imports from the UK and BNFL chief executive John Taylor has resigned.
Solution in three weeks
During his visit to Tokyo, Mr Prescott told Japan's new Prime Minister, Yoshiro Mori, that the UK would put forward a solution within three weeks.
"I expressed our deepest regret about this matter and assured the prime minister we were giving the highest priority to it," Mr Prescott told the BBC.
"In particular (we are) getting the company sorted out and getting the arrangements to improve the situation and he accepted that."
In February, BNFL admitted that staff checking the size of reprocessed Mox fuel pellets destined for Japan had faked safety records.
The fuel arrived at a sensitive time, following the major nuclear accident at Tokaimura nuclear plant which killed one worker and exposed hundreds to radioactive fall-out.
When the false safety records were revealed there was widespread public outrage.
Kansai Electric, the company which received the fuel from the UK, was furious, along with the local population near the Takahama 4 power station where the consignment was delivered.
Kansai says it no longer wants the fuel and the Japanese government has demanded it be sent back to Britain.
The row has delayed the government's plans to privatise BNFL and soured relations with Japan - which was due to be a big customer of Mox fuel.
Mr Prescott has not yet revealed how he plans to solve the dispute.