In a statement, White House spokesman Robert Gibbs also said the United States remained deeply concerned about the "deteriorating human rights situation" in Iran.
European Union leaders earlier said Iran had failed to meet its international obligations over its nuclear program, which the West suspects is aimed at developing a nuclear weapon despite Tehran's denials.
EU leaders said they would consider options for responding at their next meeting in Brussels on Jan. 21.
Gibbs said the United States echoed the "grave concerns" expressed by European leaders and that Washington remained committed to finding a diplomatic solution.
"However, if Iran continues to fail to bring its nuclear program into full compliance with the requirements of the United Nations Security Council and the IAEA, there will be consequences and we will be consulting closely with our partners to ensure those consequences are credible," Gibbs said.
The IAEA is the International Atomic Energy Agency.
Gibbs also expressed concern about the human rights situation in Iran a day after Amnesty International reported that human rights violations in Iran are as bad as at any time in the past 20 years.
"We continue to call on the Iranian government to end the use of violence and persecution against those who seek to peacefully exercise universal rights, and to abide by its international obligations, including under the International Covenant on Civil and Political rights," he said. (Reporting by Steve Holland; Editing by Paul Simao)
