Japan and India also agreed on Friday to help each other's bids for a place on the UN Security Council, as Koizumi wound up talks with Indian leaders aimed at building a new partnership.
His trip to India on Friday, the first by a Japanese prime minister in five years, came weeks after a landmark visit by Chinese Premier Wen Jiabao and is part of Tokyo's "strategic diplomacy" to compete with Beijing.
"Japan and India need each other as strong and prospering countries. Japan and India share strategic interests," Koizumi said.
Koizumi told Indian Prime Minister Manmohan Singh that Tokyo attached importance to its relations with both New Delhi and Beijing.
"I want to tell you not to worry about friendly relations between Japan and India"
Indian prime minister
Singh was quoted as saying: "I want to tell you not to worry about friendly relations between Japan and India."
India-Japan trade totalled $4.35 billion in the year ending March 2004, about one third of New Delhi's two-way trade of more than $13-billion with China.
The joint statement after the Koizumi-Singh meeting said "they reiterated their support for each other's candidature, based on the firmly shared recognition that Japan and India are legitimate candidates for permanent membership in an expanded Security Council."
"India is a nation that is full of capability and potential," Koizumi also told reporters during a visit to a local junior school which teaches Japanese to students.
Koizumi (R) briefly met Indian
President Abdul Kalam
Japan and India "must cooperate to realise the full potential of the Japan-India ties. I want to make this visit an opportunity to do that," Koizumi said.
India's Foreign Minister Natwar Singh struck a similarly upbeat note, saying he was "confident about the bright future that lies ahead for India-Japan relations" and that the Japanese leader's visit would allow both countries to take relations "qualitatively to higher levels."
Koizumi briefly met President A P J Abdul Kalam.
After spending a full day in India, Koizumi heads on Saturday to Pakistan, traditional rival of India and an ally of China.