"We will not sign any agreements unless on the first day of the implementation of the deal all economic sanctions are totally lifted on the same day," Rouhani said.
Last week, Tehran and the six powers agreed on the framework of a deal to be signed by the end of June reining in Iran's nuclear programme in return for the lifting of international sanctions.
The pace at which the sanctions will be lifted is one of the outstanding issues that still has to be agreed in the final accord.
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Western governments, which have imposed their own sanctions over and above those adopted by the United Nations, have been pushing for it to happen only gradually.
"In return for Iran's future cooperation, we and our international partners will provide relief in phases from the sanctions that have impacted Iran's economy," US Secretary of State John Kerry said last week.
Rouhani, who was speaking on Iran's National Nuclear Technology Day, reiterated that his government remained determined to develop its civil nuclear programme under the agreement with the powers.