"The fact that Iran came to the table and seemingly showed some degree of cooperation, I think, is a good thing," said James Jones, President Barack Obama's national security adviser.
"But this is not going to be an open-ended process. We want to be satisfied. We, the world community, want to be satisfied within a short period of time," Jones added. "So it's not going to be extended discussions that we're going to have before we draw our conclusions to what their real intent is. But for now, I think things are moving in the right direction."
Suspicions about Iran's nuclear intentions have risen steadily along with fears - and some evidence - that Tehran wants to build an atomic bomb and is using what it calls is a civilian nuclear energy program as cover. The Iranians are under three sets of U.N. penalties for refusing to stop enriching uranium, a key first step toward building a bomb.
"Our whole approach is predicated on an urgent need to prevent Iran from obtaining a nuclear weapons capacity," said Susan Rice, U.S. ambassador to the United Nations.
"Right now we are in a period of intense negotiations. It's not an infinite period. It's a very finite period," she said.
Rice said that in the best outcome, Iran would not have any nuclear weapons, no longer pose a threat to its neighbors or support terrorism, and treat its people with respect, allowing them to participate peacefully in a democratic process. "That's the Iran we hope to see."
Current penalties have failed to change Tehran's course and have been watered down through efforts by Russia and China. Those countries, along with the U.S., Britain and France, can block action in the Security Council.
Rice said the U.S. had three options: to push sanctions through the U.N.; work with European allies to punish Iran; or to take unilateral action in conjunction with the other possible courses of action.
Members of Congress are ready to authorize steps the U.S. can take against Iran, in addition to possible U.N. action.
Sen. Bob Casey, D-Pa., said the U.S. "cannot allow talking and negotiation to replace strong action if we feel we have to take that step."
Sen. Lindsey Graham, R-S.C., said he would like Congress to pass measures that would "empower the president and our country to be tough and to put some actions behind words. So let's have 'Iran Week' in the Senate and get something done."
Lawmakers are talking about trying to block gas and refined petroleum exports to Iran, possibly causing serious disruptions in the lives of ordinary Iranians. Others moves could affect Iran's financial institutions and impose new trade bans.
Iran is a major oil producer but imports gasoline and refined petroleum products.
Obama has said his administration, in conjunction with Congress, is crafting plans that could target Iran's energy, financial and telecommunications sectors.
The second-ranking Senate Republican, Arizona's Jon Kyl, said" putting sticks on the table is exactly the point." He said the Iranians "never respond to anything except pressure."
Jones and Kyl were on CNN's "State of the Union," Rice spoke on NBC's "Meet the Press," and Casey and Graham were on "Fox News Sunday."