Philip Crowley said Iran should ease international concern over its nuclear programme
The US says it is unhappy with the package of proposals submitted by Iran on Wednesday aimed at breaking the deadlock over its nuclear ambitions.
A senior US State Department official said the measures do not address the status of Iran's nuclear programme.
The US wants Iran to suspend its uranium enrichment programme which it says could be used for nuclear weapons.
Russia was more positive about the proposals and ruled out the possibility of sanctions on Iran's oil sector.
Russian Foreign Minister Sergei Lavrov said the proposals offered something to work with.
Iran has always insisted its nuclear programme is for civilian purposes only.
In its five-page proposal, Tehran offers to hold "comprehensive, all-encompassing and constructive" negotiations on a range of security issues, including global nuclear disarmament.
But the document, delivered to Western powers on Wednesday, makes no mention of Iran's own nuclear programme.
On Wednesday, the US envoy to the International Atomic Energy Agency (IAEA), Glyn Davies, said Iran could already have enough low-enriched uranium to produce a bomb, if it was further enriched.
"Our concern is that the response itself did not really address what is the core issue of the international community and the core concern, which is Iran's nuclear ambitions," Philip Crowley, the US Assistant Secretary of State for Public Affairs, told the BBC's World Today programme.
Some of the sanctions under discussion... are a step to a full-blown blockade and I do not think they would be supported at the UN Security Council
Sergei Lavrov Russian Foreign Minister
Mr Crowley said Iran had to prove it was ready to live up to commitments it had made.
"One of the questions going forward will be to test the Iranian interest in actual engagement, either with the United States or the international community and obviously a core concern is in fact its nuclear programme," he said.
But Russia's foreign minister saw the Iranian proposals as a positive step forward.
"Based on a brief review of the Iranian papers my impression is there is something there to use," Sergei Lavrov said in Moscow.
"The most important thing is (that) Iran is ready for a comprehensive discussion of the situation, what positive role it can play in Iraq, Afghanistan and the region."
Iran's proposals have been published on the website of ProPublica, a US-based independent, non-profit newsroom that produces investigative journalism.
Among other things, Tehran calls for an end to hostilities and talks on issues such as drug trafficking, security in the Middle East and Afghanistan.
Iran insists its rocket building programme is for satellites
Iran hopes the proposals - to be reviewed by the five permanent UN Security Council members and Germany on Friday - will head off new international sanctions.
Mr Lavrov said he did not think the UN Security Council would support oil sanctions against Iran.
"Some of the sanctions under discussion, including oil and oil products, are not a mechanism to force Iran to co-operate, they are a step to a full-blown blockade and I do not think they would be supported at the UN Security Council," he said.
But US President Barack Obama warned Tehran earlier this year that, unless Washington saw a positive response to its friendlier overtures by the end of September, he would be prepared to press for new sanctions against Iran.
The BBC's Bridget Kendall, in Moscow, says Mr Lavrov's comments leave little doubt that Russian and Western approaches to Iran continue to diverge.
Finding common ground for a united response to the latest Iranian proposals may prove tricky, she adds.
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