Aso spoke to his Iranian counterpart Manouchehr Mottaki by telephone two days after the UN Security Council unanimously approved a resolution imposing sanctions that target Iran's sensitive nuclear and ballistic missile programs.
"Our minister called on Iran to suspend all activities of uranium enrichment," a foreign ministry official said.
"It is important to seek a peaceful and diplomatic resolution," he said. "For that purpose, there is no way but to accept the UN resolution and return to the negotiating table."
Mottaki was quoted as replying: "The UN resolution is to strip our country of due rights. It was very regrettable."
Japan, despite being a close US ally, has maintained close trade ties with Iran. Asia's largest economy is almost entirely dependent on the Middle East for its oil, and imports about 15 percent of its total oil consumption from Iran.
Japan in 2004 defied the United States by signing a two-billion-dollar deal to develop Iran's largest onshore oil field.
But in the build-up to the imposition of UN sanctions, Japan slashed its stake in the Azadegan project to 10 percent from the originally agreed 75 percent.
Western countries backed the sanctions, fearing Iran could use uranium enrichment activities to develop nuclear weapons. Iran, which says its program is for peaceful purposes, vowed to expand its enrichment.