Miss Clark arrived in Tokyo today on her first bilateral visit in three years.
Greenpeace Japan's whale project leader Junichi Sato said Miss Clark needed to make whaling the central issue of talks with Mr Fukuda and "agreeing to disagree", as the two countries had done in the past was no longer enough.
"Agreeing to disagree does not resolve any issues and now the issue is getting more complicated with more whales getting killed," he told NZPA.
"Japan has been raising the number of the hunt for the last three years. So it's not the same situation as when Helen Clark came to visit Japan three years ago.
"It has to be changed and she needs to be stronger."
Mr Sato said Greenpeace would like to see New Zealand make an offer to Japan to collaborate in a non-lethal whaling research programme in the Southern Ocean as a replacement for Japan's scientific whaling programme, which this year had an upper catch limit of 850 Minke and 50 Fin whales.
Miss Clark has said she will raise the issue with Mr Fukuda, but has not specified in what terms.
The issue has the potential to complicate the relationship on a trip in which Miss Clark is keen to seek some kind of commitment from Mr Fukuda to boost ties.
Miss Clark today visited the Toshogu Shrine at Nikko, near Tokyo, which has long-standing links with New Zealand.
The shrine, built by the Tokugawa Shoguns and one of the most famous in Japan, was gifted a white horse - which is viewed as sacred and carries out ceremonial duties - from New Zealand in 1972. Since then it has received three replacements, the last gifted by Miss Clark in 2005.
The horses are seen as symbolic of the friendship between the two countries.
At the shrine Miss Clark viewed a dance performance and took part in a brief tea ceremony.
While in Japan, Miss Clark will also attend the inaugural Japan-New Zealand Partnership Forum - a high-level business event aimed at refocusing Japanese attention on New Zealand.
She then flies to Korea where she is expected to discuss the likelihood of free trade negotiations with South Korean president Lee Myung-Bak on Friday. - By Grant Fleming/NZPA
- Grant Fleming travelled to Japan with the help of the Asia New Zealand Foundation.
