South Korea has often-prickly ties with its former colonial ruler. A decades-old row over disputed islands in the Sea of Japan (East Sea) resurfaced this summer.
Mr Aso, president of the ruling Liberal Democratic Party, was elected as new prime minister on Wednesday to replace Mr Yasuo Fukuda.
'I wish South Korea and Japan will further improve their relations following the election of Mr Aso as the new Japanese prime minister,' Mr Lee said in the message.
'Bilateral relations must be developed in a future oriented direction and with history in mind. That will be essential to the stability and prosperity of North-east Asia.' -- AFP