Indonesia has the world's largest population of Muslims, the majority of whom are Sunnis, but it seldom plays a prominent role in the Islamic world.
Uneasy relations between the conservative Sunni kingdom of Saudi Arabia and Shi'ite power Iran deteriorated sharply when Saudi Arabia executed Shi'ite cleric Nimr al-Nimr on January 2, triggering outrage among Shi'ites.
Saudi Arabia cut ties with Iran after protesters attacked the Saudi embassy there.
Indonesian Foreign Minister Retno Marsudi will travel to the Middle East this week to meet heads of state of the rivals, both of which are major oil exporters.
"Indonesia is ready to play a role to help the process and whatever needs to be done to maintain peace and stability in the region," ministry spokesman Armanatha Nasir told Reuters.
"Because if it is not maintained, the impact is not just for the region, but there will be a global impact," he said.
Indonesia hoped the two sides could resolve their difference amicably, he said.
Indonesia has seen sporadic attacks on its Shi'ite minority in recent years and analysts say there is a risk of increasing threats against the community given the tension in the Middle East.
Anti-terrorism police in recent days arrested four men suspected of planning attacks on prominent Indonesian Shi'ite leaders.
Officials believe there are more than 1,000 supporters of the hardline Sunni group Islamic State (ISIS) in Indonesia, and say that scores of Indonesian ISIS activists have returned from the Middle East