The decision comes despite the opposition of President Mahmud Ahmadinejad.
State-run radio said that under the bill, the government will inspect and fingerprint all U.S. nationals entering the country.
The measure still needs to be approved by the country's constitutional watchdog, the Guardian Council, before it can become law.
Ahmadinejad last month said he is against the bill because his administration has no dispute with ordinary Americans.
RFE/RL Iran Report
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