The two were detained separately in May while visiting Iran and were accused of being involved in efforts to carry out a US-backed "velvet revolution" there.
Both have been charged with espionage and endangering national security.
"One of my missions was to identify speech-makers"
Haleh Esfandiari, detained Iranian-American
Washington, which broke ties with Iran in 1980, has rejected the accusations and called for their release.
In the clip aired on Monday, Esfandiari, an academic at the US-based Woodrow Wilson International Centre for Scholars, said she was "an element" in Georgia's velvet revolution.
"One of my missions was to identify speech-makers...," she said in the clip, apparently part of a confession.
Esfandiari, who was wearing in a black headscarf, added: "In the name of dialogue, in the name of women's rights, in the name of democracy."
Lee Hamilton, president of the Woodrow Wilson Centre, described the charges against Esfandiari as ludicrous and said she was being held in solitary confinement.
|Tajbakhsh said in the clip his organisation might |
have been targeting the Islamic world [Reuters]
Tajbakhsh, a consultant with the Open Society Institute founded by billionaire investor George Soros, said in the video that his foundation "might have been targeting Islam".
He was shown holding notes and saying "[The role] of the Soros centre after the collapse of communism was to focus on the Islamic world".
Iran TV said the full programme In the Name of Democracy would be broadcast on Wednesday and Thursday evenings.
The station has in the past broadcast what it said were confessions of dissidents serving jail sentences for alleged attempts to undermine Iran.
"To prevent these kinds of people from leaving Iran sends a negative message and is an unfortunate comment"
Sean McCormack, US state department
A US state department spokesman said he had not seen the television images of Esfandiari and Tajbakhsh but said they should be allowed to leave immediately.
"They should all be allowed to leave Iran and be reunited with their families," said Sean McCormack.
"To prevent these kinds of people from leaving Iran sends a negative message and is an unfortunate comment about the nature of this particular regime."
Ayatollah Ali Khamenei, Iran's supreme leader, has warned of a US-backed "velvet revolution" using intellectuals and others to bring about "regime change".
Two other Iranian-Americans have been charged with security-related issues. One of them has been freed on bail.
Ramin Jahanbeglou, an Iranian-Canadian writer detained for four months last year for endangering state security, was also shown in Monday's promotional clip saying: "I had ties with American political institutes."
Rights groups and Western diplomats say Iran is cracking down with increasing rigour on dissidents, intellectuals and critical journalists, adding that it may in part be a response to international pressure over its atomic programme.