"The Iranians are deeply concerned about respect, the one thing they yearn for is respect," Jim Slattery, 66, said at a presentation at the Atlantic Council think-tank.
His Iranian hosts, he said, assured Slattery he was the first US lawmaker invited to the country since the Islamic Revolution ousted the Washington-backed shah.
The Kansas Democrat, who served in the House of Representatives from 1983 to 1995, attended an international conference in Tehran against violence and extremism.
He also met with Iranian officials, including key members of Parliament.
President Hassan Rouhani and his inner circle are "deeply committed to improving this relationship with the United States," he said.
"And I believe that if they fail, we are likely to see the return of a much more hard-line government in Iran."
The visit was particularly timely in that it occurred in the midst of intense international negotiations on resolving a long-running dispute over Iran's nuclear operations.
The Iranian officials he met were "all deeply concerned about what effect Congress elections last November will have on President (Barack) Obama's capacity to actually implement any agreement" on reining in Iran's nuclear program.
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"They are very troubled by the prospect of... putting their best deal on the table," only to have US lawmakers reject it.
"This would be a political disaster," Slattery added. "So they need assurances that if there is a deal that is worked out, they want to be confident that it can actually be approved and implemented by the Obama administration."
November's elections gave Republicans full control of Congress, and several lawmakers seek to challenge Obama by passing legislation imposing new sanctions against Iran before conclusion of the nuclear negotiations.
Slattery argued that both Tehran and Washington bore responsibility for obstacles to an international deal.
"Very few members of our administration... have any personal relationships with Iranians," he stressed.
"One of the great problems we have to overcome right now is ignorance."
Slattery suggested a path for dialogue through religion, a dominant force in the two countries.
"Religion is a big part of their life, just as it is in Kansas," he said.
"Isn't there a space here for conversation?"