Modi, who was welcomed at a ceremony commemorating Indian independence activist Mahatma Gandhi, said defense cooperation between the two sides is emerging as a major aspect of a special strategic partnership, South Korean newspaper Chosun Ilbo reported.
The Indian prime minister said there is potential for further cooperation in the defense field, according to the report.
Modi is visiting Korea less than a year after Moon paid a state visit to one of the world's fastest growing economies, which included a stopover at Gandhi Memorial Hall.
On Thursday, Moon unveiled a bust of Gandhi at Seoul's Yonsei University and spoke of his reverence for Gandhi's "life and philosophy," according to Donga Ilbo and other reports.
"Gandhi did not succumb to any violence or threats, but walked on the side of truth, and on the side of peace," Moon said. "Gandhi's belief a people can overcome all forms of oppression if they stand up for themselves brought the people of India together and ultimately won their independence and freedom."
Referring to a shared experience of colonialism under different imperial powers, Moon said the two countries should work to establish peace and prosperity in Asia in a year that marks the 150th birth anniversary of Gandhi as well as Korea's March First Movement.
Modi, who is in Korea for two days, is encouraging businesses to invest in India.
The Indian prime minister said his government has introduced a start-up policy that is open to direct investment, according to All India Radio.
Modi also told the Chosun Ilbo South Korea's example of economic development has served as a benchmark for his country.
"We want to learn from Korea," he said.
India is expected by the end of 2019 to surpass Britain and France to become the fifth-largest economy in the world, according to Center for Economics and Business Research in Britain.
Modi is up for re-election in 2019.