US State Department spokesman Sean McCormack said the resolution, which passed 14 to 1, is meant to compel Tehran back to the negotiating table.
The Security Council gave Tehran an August 31 deadline to comply. If it does not, Iran will head "down the road of further isolation," said Mr McCormack.
"The international community has offered them a pathway ... so that we can have negotiations," said Mr McCormack.
"They don't have anywhere to hide. They don't have any protectors," he said.
"It is in their interest, it is in the interest of the international community for them to comply."
Resolution rebuffed
Iran's ambassador, Javad Zarif, rebuffed the resolution in a 30-minute speech to the council, accusing the United States and its European allies of "imposing a destructive and totally unwarranted Security Council resolution".
"I would suggest to you that this approach will not lead to any productive outcome. It can only exacerbate the situation," he told the council, adding that Iran was ready for "serious and non-discriminatory" negotiations.
Iran had earlier threatened to reject an offer of international economic and political incentives to stop its uranium enrichment if the Security Council passes the resolution.
But the ambassadors for Britain, France and Germany, which have led negotiations with Iran, emphasised that there was still a possibility to negotiate a settlement, and renewed calls for Tehran to accept the incentives package.
US Resolution 1696, adopted on Monday, expresses "serious concern" over Iran's refusal to comply with International Atomic Energy Agency (IAEA) orders to halt uranium enrichment and other work that could lead to developing a nuclear bomb.
No immediate threat
The text of the resolution stopped short of an immediate threat of sanctions, which have been opposed by Russia and China, and said punitive action would have to be the subject of further discussions.
But if Iran does not suspend its nuclear work by the deadline, the Security Council will move to debate a new resolution that could order economic and political sanctions.
Qatar was the only council member to oppose the resolution, arguing it was too confrontational. "Do we really want to see another volcano erupting in this region," questioned Qatari Ambassador Nassir Abdulaziz al-Nasser.
The resolution was proposed by Britain, France and Germany, with strong US backing.
All suspect Iran's nuclear programme hides covert efforts to build a nuclear bomb, although Tehran says its research is for peaceful purposes.
Russia and China gave their backing to the resolution, though both insisted that there was no immediate threat of sanctions.