Abe made the promise as he held talks with his Bangladesh counterpart Sheikh Hasina who arrived in Tokyo yesterday, the foreign ministry said.
Japan will provide Bangladesh with assistance worth up to USD 5.9 billion, mainly government loans, over four or five years, a statement said.
The sum will include a loan package totalling 120 billion yen which was promised by Japanese Foreign Minister Fumio Kishida during his visit to Bangladesh in March.
The multi-year assistance is expected to cover public works such as construction of roads and power plants, local media said.
"In order to realise its potential and expedite further growth, Japan has come up with the concept of the Bay of Bengal industrial growth belt," he said.
Hasina, who met Emperor Akihito earlier in the day, is scheduled to stay in Japan until Wednesday.