It showed a large majority of the population in favour of dialogue with the "Great Satan" and nearly half showing sympathy with US policy on Iran.
The conservative judiciary has shut down a state-run polling institute and is taking both its director and the head of the state news agency Irna - which published the poll - to court.
The reformist-dominated national parliament, which commissioned the poll, has defended it and called for the prosecutions to be dropped.
According to the poll of 1,500 Iranians, conducted by three separate institutes including the National Institute for Research Studies and Opinion Polls (NIRSOP) and published by Irna on 22 September:
Mr Nasseri has already appeared in court while Mr Geranpayeh's institute was sealed off by court officials on Monday as he faced his appearance.
'Valid poll'
The parliament, or Majlis, confirmed on Wednesday that it had commissioned the poll as part of a study of ties with the US.
Its presiding board sent a letter to the chief of the judiciary, Ayatollah Majmoud Hashemi-Shahroudi, demanding a halt to the prosecutions.
One MP, Ahmad Burqani, stressed that the poll had been conducted by three separate institutes.
"The fact that the results are similar shows they have been conducted correctly," he told Irna.
A spokesman for the government of reformist President Mohammed Khatami, Abdollah Ramazanzadeh, described NIRSOP as "one of the most credible" in Iran.
"It has done nothing wrong - it just carried out a poll that was ordered by parliament," he said.
Tensions have simmered for years in Islamic Iran between the conservative clergy led by spiritual leader Ayatollah Ali Khamenei and the elected president.
Relations with the US are a particularly thorny issue after the Islamic Revolution in 1979 led to a dramatic split with Washington, typified by the Tehran hostage crisis.
The parliament called for a new dialogue with Washington earlier in the year after relations appeared to dip when President George W Bush ascribed Iran to a global "axis of evil".