TOKYO (Reuters) - Japanese Prime Minister Shinzo Abe will seek Cuba's help in responding to North Korea's nuclear and missile programmes during a rare visit to Havana next week, a spokesman said, and also hopes to expand Japanese business interests on the island.

Abe will become the first Japanese leader to visit Communist-ruled Cuba, which is one of North Korea's few diplomatic allies and is also slowly re-emerging after decades of international isolation and a U.S. trade embargo.

His trip follows the normalisation of ties last year between Cuba and the United States, former Cold War enemies, and U.S. President Barack Obama's visit to Cuba earlier this year.

Japan, South Korea and the United States have been strengthening their alliance since last week's nuclear test by North Korea, its fifth and largest, which alarmed its East Asian neighbours.

"We would like to seek Cuba's understanding and cooperation for the resolution of North Korea-related issues such as abduction (of Japanese citizens), nuclear and missiles," Chief Cabinet Secretary Yoshihide Suga told a regular news conference on Wednesday.

The United States has called for a swift and strong United Nations response to Pyongyang, while its envoy on North Korea has said Washington remained open to meaningful dialogue with the North to end its pursuit of nuclear weapons.

Japan is also keen to build business ties with Cuba, which began normalising relations with the United States in December 2014, before full diplomatic ties were restored.

More than 100 U.S. business delegations have visited Cuba since 2014, although many U.S. companies say the decades-old trade embargo makes business almost impossible.

"We aim to support Japanese companies' expansion there by encouraging Cuba, which has attracted global attention since the resumption of diplomatic ties with the United States last year, to improve its business and investment environment," Suga said.

Last week, Japan's Kyodo news agency reported that Abe had decided to forgive two-thirds of Cuba's 180-billion-yen (£1.3 billion) debt to Japan, as Tokyo seeks to build closereconomic ties.

Abe will formally announce the offer during his meeting with Cuban President Raul Castro, Kyodo reported.

Chinese Premier Li Keqiang will also visit Cuba, on a trip from Sunday until Sept. 28 that includes the United Nations General Assembly and Canada, but China's foreign ministry has not unveiled the Cuba visit dates.

Chinese President Xi Jinping visited Cuba in 2014, signing several investment deals between the two Communist-led countries.

(Reporting by Kiyoshi Takenaka; Additional reporting by Michael Martina in Beijing; Editing by Clarence Fernandez and Paul Tait)