The interim agreement, which came into force on Monday, was reached with the US, Russia, China and European powers in November.
The nuclear deal is designed to prevent Iran from developing atomic weapons. Tehran denies trying to do so, saying its nuclear programme is solely for peaceful purposes.
The agreement followed months of secret talks between Iranian and US officials, and aims to provide breathing space until a more permanent deal can be reached.
Mr Amano, who is director general of the International Atomic Energy Agency, was speaking at a meeting of the organisation’s governors in Vienna.
The agency has estimated that the extra workload generated under the terms of the deal would cost around 6m euros ($8.2m; £4.9m).
Mr Amano asked the board to endorse the IAEA “undertaking monitoring and verification in relation to the nuclear related matters set out in the Joint Plan of Action, subject to the availability of funds”.
He said: “This will be a further important step towards achieving a comprehensive solution to the Iran nuclear issue.
“But there is still a long way to go.”