The US has said it could still refer Iran to the UN Security Council, even though nuclear inspectors said Tehran had fully suspended uranium enrichment.
Iran says its nuclear ambitions are peaceful - mainly to produce energy
The International Atomic Energy Agency (IAEA) said 20 disputed centrifuges had now been included in Iran's freeze.
It passed a resolution welcoming the suspension, but containing no threat to send Iran to the UN Security Council if it resumes enrichment.
The White House said it maintained the right to refer Iran unilaterally.
White House spokesman Scott McClellan said: "The implementation and verification of the agreement is critical."
"Iran has failed to comply with its commitments many times over the course of the past year and a half," he added.
The US accuses Iran of planning to build nuclear weapons. Iran denies the accusations, saying its programme will be used solely for energy production.
Last week it had sought to have 20 centrifuges exempted from the agreement to suspend enrichment, but dropped the demand at the weekend.
Earlier on Monday, IAEA Director General Mohamed ElBaradei said: "We have already verified these 20 centrifuges and they are under agency surveillance."
"We have now therefore completed our verification of Iran's decision to suspend enrichment and reprocessing-related activities."
The IAEA board of directors then passed the resolution welcoming Iran's move.
The BBC's Bethany Bell in Vienna says the resolution makes a key concession to Tehran, by calling the suspension a voluntary, confidence-building measure, that is not legally binding.
Months of wrangling
Although the resolution does not threaten to send Iran to the UN Security Council if it resumes enrichment it is said to propose that Mr ElBaradei "report immediately" to the board if there is any evidence of incomplete suspension.
Over the weekend, and after months of wrangling, Tehran backed down from its demand that some centrifuges not be included in the freeze, saying they would not be used.
The Iranian authorities added, however, that the centrifuges would not be sealed by the IAEA, but would instead be monitored by cameras.
Centrifuges can be used to enrich uranium for use as fuel in power plants or weapons.
The US has led the calls for Iran to be referred to the UN Security Council, which could impose sanctions on Tehran.
The European Union, led by Britain, Germany and France, have been pressing for a diplomatic solution rather than sanctions.
China, a permanent member of the Security Council with the power of veto over its resolutions, has said it strongly opposes referral to the council.