President Hassan Rouhani and the secretary of the Supreme National Security Council, Ali Shamkhani, made the comments during talks in Tehran with the prime minister of Iraq's Kurdish autonomous region.
Rouhani told Nechirvan Barzani that Tehran backs "a united Iraq" in which "the legal and legitimate rights" of the Kurdish people are recognised in line with the constitution, the presidency said.
Shamkhani said Tehran "will do everything in its power to support efforts to ease the differences" between Baghdad and the Kurdish regional capital Arbil, official IRNA news agency reported.
The referendum was also condemned in neighbouring Iran and Turkey.
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Yesterday, Barzani met Iraqi Prime Minister Haider al- Abadi in Baghdad for the first time since the failed push by the Kurds to secede.
A statement from Abadi's office said they discussed the "political and security situation and ways of settling disputes".
After September's vote, Baghdad imposed an air blockade on international flights to the Kurdish autonomous region's two main airports and retook disputed areas, including oil fields from which the Kurds derived the bulk of their revenue.