"If there is no end to sanctions, there will not be an agreement," Rouhani said in a televised speech in the northern city of Rasht.
"The end of these negotiations and a signed deal must include a declaration of cancelling the oppressive sanctions on the great nation of Iran, IRNA reports.
"We are in talks with the major powers and not with the Congress," he said, adding Iran wanted to end its isolation by having "constructive interaction with the world and not confrontation".
"Rouhani also said the U.S. Congress' power to review a nuclear deal with Iran is domestic matter.
"We are in talks with the major powers and not with the Congress," he said, adding Iran wanted to have "constructive interaction with the world and not confrontation".
Meanwhile US Secretary of State John Kerry said Wednesday he is still confident that the U.S. administration can conclude a nuclear deal with Iran after US President Obama agreed to sign legislation giving Congress the right to reject an agreement, CBS News reports.
"Yesterday there was a compromise reached in Washington regarding congressional input," Kerry told reporters in the Baltic Sea port of Luebeck. "We are confident about our ability for the president to negotiate an agreement, and to do so with the ability to make the world safer."