The head of the United Nations nuclear watchdog is due to visit Iran on October 29 for talks with senior officials there, as opposition from the United States threatens to undermine a landmark worldwide agreement to limit Iran's nuclear program.
Amano made the remarks in a press conference with Iran's nuclear chief Ali Akbar Salehi.
Mr Rouhani spoke days after the US House of Representatives voted for new sanctions on Iran's ballistic missile programme, part of an effort to clamp down on Tehran without immediately moving to undermine an global nuclear agreement.
He said that he has held good negotiations with the IAEA head, underling that Amano's trip at this sensitive juncture has a specific message and IAEA's role is fully certain in this regard.More news: Kyle Long suffers hand injury as Bears' offense continues to struggle
A statement Sunday from President Hassan Rouhani's office quoted him as telling Yukiya Amano that Iran's adherence to the deal "has been complete and remarkable". Amano is determined to play his important role in this sensitive period, he said.
US President Donald Trump earlier this month refused to certify that Iran was living up to the 2015 nuclear agreement with Western nations, and Iranian leaders have refused to back off plans to continue work on long-range missile programmes.
Prior to the meeting with Amano, Iran's president excoriated USA policies before his country's parliament.
Amano is in Tehran for talks with the Iranian senior officials focusing on the verification and monitoring of the implementation of the 2015 nuclear agreement.More news: Twitter overcounted active users since 2014, shares surge
"We have built, are building and will continue to build missiles, and this violates no worldwide agreements", Rouhani was quoted by State TV, as saying.
The IAEA is in charge of monitoring restrictions on Iran's nuclear program under the nuclear agreement.
Salehi said that Iran could resume uranium enrichment of 20% within four days if it wished.
Commenting on Trump's recent claims about possible unilateral withdrawal from the JCPOA, the president said that the incumbent U.S. administration showed that it had "lack of commitment to an worldwide agreement" and did not respect negotiations and accords, adding that such country can not be trusted.More news: Tottenham Hotspur forward Harry Kane to miss Manchester United clash
Under the deal, Iran is allowed to enrich uranium to low levels of 3.5%, which can be used to power reactors.