Several nations, including the United States, believe that the enrichment programme is part of an effort to to produce nuclear weapons, but Tehran says it simply wants the technology to help it meet civilian energy needs.
In a news conference in Vienna earlier on Friday, Amano said that Iran, like other countries, is under obligation to implement Security Council resolutions.
"I hope the implementation by Iran and other countries will further help the agency to discharge its responsibilities," he said.
Mohamed ElBaradei, who Amano is replacing as head of the IAEA, told the UK-based BBC broadcaster last month that he had a "gut feeling" that Iran was seeking the ability to produce nuclear arms.
He said that perceived threats from neighbouring countries and the United States could encourage Tehran to work towards weapons of mass destruction as an "insurance policy".
Amano, a lawyer who graduated from Tokyo University and joined Japan's foreign ministry in 1972, will succeed ElBaradei in November.
Amano has extensive experience negotiating nuclear safeguards agreements thoughout his diplomatic career.