The Jakarta governor, who won a resounding electoral victory last month, told Japan's Asahi newspaper that he would work toward finding diplomatic, not military, solutions to the simmering conflicts.
Beijing claims almost all of the South China Sea, putting it at odds with countries including the Philippines and Vietnam, and there have been several tense encounters in the area over recent months.
"We're hoping for diplomatic solutions and, if necessary, Indonesia stands ready to play an intermediary role," Widodo said, according to the Asahi interview published in Japanese.
Indonesia does not have any disputes with China over the South China Sea, and has traditionally held a mediating role in rows over the waters.
Widodo also said he would help speed up the drafting of a code of conduct between China and the 10 member states of the Association of Southeast Asian Nations (ASEAN).
His comments come as Beijing accused Washington of deliberately stoking tensions in the South China Sea, and rejected Washington's proposal for a freeze on provocative actions in the region.
By Ruchi Singh