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, which was published in Japanese.
"I refuse to accept a military solution," he added.
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.
The remarks by Foreign Minister Wang Yi came at an Asean Regional Forum at the weekend overshadowed by disputes in the strategically significant waters.
Asean members have shown varying degrees of alarm to China's growing assertiveness in the region.
Tensions escalated after China positioned an oil rig in an area also claimed by Vietnam, with each country accusing the other of ramming its ships.