The prime minister held a telephone conversation with Lee Myung-Bak, the president of South Korea, after the release of the statement.
South Korea gave a guarded welcome to the statement, saying it hoped the apology marked the start of an era of closer relations between the two countries.
Japanese prime ministers in recent decades have expressed regret for the country's wartime aggression in Asia, including a landmark 1995 statement from then prime minister Tomiichi Murayama.
But such sentiments have been dismissed as insincere by Asian neighbours, partly because of comments made by some conservative lawmakers who refuse to admit to Japan's past aggression.
Kan said on Tuesday that he sought to "build a future-oriented relationship" with South Korea. Tokyo is looking to strengthen cooperation in addressing the North Korea's nuclear ambitions and abductions of foreign nationals.
"In this 21st century Japan and South Korea are the most important and close neighbours who share democracy, freedom, market economies and other values," he said.
Japan colonised Korea from 1910, signing an annexation treaty on August 22 which took effect on August 29 that year.
The annexation ended on August 15, 1945, when Japan surrendered to the US-led allies in World War II.
The Korean peninsula then split into the communist North and capitalist South.
Japan and South Korea normalised relations in 1965 with Tokyo extending massive economic aid to Seoul, which agreed not to demand reparations for the colonial rule.