"I think that the IAEA (International Atomic Energy Agency) board of governors sent a very clear message that Iran must cease its pursuit of nuclear weapons and answer questions which the board has raised and suspend its enrichment activity," Abraham told reporters in Vienna.
He said Washington's view was "that Iran should follow the obligations and cooperate fully with the IAEA. The clock is ticking down now on Iran to the next meeting" of the IAEA board in November.
Sunday, Iran reacted with defiance to the adoption of the resolution at a meeting of the agency's board in Vienna Saturday.
"Iran will not accept any obligations concerning the suspension of enrichment," Iran's top nuclear official Hassan Rowhani told a press conference in Tehran.
Although Rowhani appeared to reject Saturday's resolution, he did say that Iran could accept a suspension "through negotiations" and if it was a "voluntary decision".
But he also raised the tone of the stand-off by warning that the Islamic republic would halt its application of a key safeguards treaty if the nuclear dossier was referred to the UN Security Council, as sought by the United States.
The Islamic regime insists its nuclear programme is strictly aimed at generating electricity, despite suspicions it is seeking to develop the capability to build nuclear weapons.
Uranium is enriched through centrifuges to make what can be fuel for civilian nuclear reactors but also the explosive material for atomic bombs.
Enrichment is allowed under the nuclear Non-Proliferation Treaty (NPT), which sets the safeguards requirements that the IAEA monitors, but Iran had agreed with Britain, France and Germany in October 2003 to suspend enrichment as a confidence-building gesture.
Iran has insisted from the beginning, however, that this is a voluntary and temporary measure, and that it can begin enrichment activities if and when it sees fit.
Despite suspending actual enrichment, Iran has continued support activities such as building the centrifuges that refine the uranium.
It recently alarmed the United States by saying that it would be carrying out the first stage of the nuclear fuel cycle, making the uranium gas that is the feed for centrifuges.