According to the Kyodo news agency, Suga has also congratulated Biden on his victory in the presidential election, which is disputed by incumbent President Donald Trump.
After their first phone talk, Suga told reporters that he conveyed to Biden his desire to deepen cooperation between the countries in order to realize a "free and open Indo-Pacific" region.
The leaders have also agreed to coordinate efforts on global challenges, such as fighting the COVID-19 pandemic and climate change.
They also agreed that the visit of Suga to the United States would take place as soon as possible. Possible dates of the visit have not been mentioned.
After World War II, the Senkaku Islands went under the control of the United States and were later passed to Japan in 1972. Japan believes that China's sovereignty claims over the islands follow the discovery of valuable minerals in their shelf water in the 1970s. The territorial dispute escalated in 2012, when the Japanese government purchased three of the five islands from a private owner, thus establishing Tokyo's sovereign ownership.