On July 10, Iran said it has new evidence linked with national security charges against both.
"Whatever purported evidence that they have come up with is about as credible as their previous evidences. That has no basis," said spokesman Sean McCormack. "These are people, and especially in the case of Mrs Esfandiari, people that have tried to build bridges between the Iranian people and the outside world."
Esfandiari, the head of the Middle East program at the Woodrow Wilson International Center for Scholars, was arrested in May after returning to Iran late last year to visit her elderly mother.
In May, Esfandiari and Tajbakhsh, along with a third U.S.-Iranian, journalist Parnaz Azima, were charged with acting against Iran's national security.
The Iranian judiciary July 10 did not elaborate on the case of Azima, who is free on bail, or that of U.S.-Iranian peace activist Ali Shakeri, who is detained on security-related charges.