Tehran, however, insists the programme is only aimed at generating electricity.
The UN Security Council has adopted four resolutions, three of which included the imposition of sanctions, requiring Iran to suspend uranium enrichment.
Rice said the US remained "deeply concerned about the threat that Iran's nuclear programme poses to the region, indeed to the United States and to the entire international community."
"We will look at what is necessary and appropriate with respect to maintaining pressure toward that goal of ending Iran's nuclear programme," she added.
"Dialogue and diplomacy must go hand in hand with a very firm message from the United States and the international community that Iran needs to meet its obligations as defined by the Security Council and its continued refusal to do so will only cause pressure to increase," Rice added.
During his election campaign, Barack Obama, the US president, said he would consider holding direct talks with Iran and other powers with poor relations with the US.
Robert Gibbs, a White House spokesman, said on Monday the US would use "all elements of our national power" to address its concerns about Iran's nuclear programme.
He said Rice's comments were not a new initiative and that Rice was simply restating comments made by Obama on the presidential campaign trail.