"There is no production at all ... As right now there is no need for the production of 20 per cent (enriched) uranium," the parliament website reported conservative MP Hossein Naqavi Hosseini as saying.
Iran's nuclear enrichment programme is at the core of its dispute with world powers, who suspect it masks a drive for atomic weapons despite repeated denials by the Islamic republic.
Enriching uranium to 20 per cent purity is a few technical steps short of producing weapons-grade fissile material.
Iran's nuclear enrichment activities are monitored by the UN nuclear watchdog, the International Atomic Energy Agency (IAEA).
The Vienna-based agency said it was aware of the report but had no comment on it.
"We're aware of this report but I'm afraid we're not commenting right now," IAEA spokeswoman Gill Tudor told AFP via email.
The parliamentary website, ICANA.Ir, further quoted Naqavi Hosseini as saying the fuel for the Tehran reactor, which is used to produce medical isotopes, is fully stocked.
"Tehran itself decides whether to have above five percent enrichment or not. But the issue of suspension and halt is at the moment meaningless as there is no production at all," he said, referring to Western demands that Tehran suspends the high-level enrichment.
Naqavi Hosseini is spokesman for the foreign policy commission, which is regularly briefed on Iran's nuclear work.
Declarations by members of the commission have on occasions been denied by the government.
All decisions on Iran's nuclear programme rest with the ultimate decision-maker, supreme leader Ayatollah Ali Khamenei.
