"It makes sense not to add new sanctions while negotiations are going on," Sen. Chuck Schumer, D-N.Y., was quoted by The New York Times as saying after he and nine other top Democratic and Republican leaders of Senate foreign policy and national security committees met with President Obama at the White House.
At the same time, the senators urged Obama to reject any nuclear deal with Iran that did not include a tangible rollback of its nuclear weapons program, the senators told reporters.
The talks in Geneva, billed as picking up where failed talks in the Swiss city left off 10 days ago, are to pursue what officials call a "first-step," six-month agreement in which Iran freezes its nuclear program in return for a moderate letup of economic sanctions.
The proposed interim deal has met fierce opposition from Israel and Persian Gulf allies, as well as from Republicans and some Democrats in Congress.
Under the proposed deal, during the six months, the United States, Britain, France, Germany Russia and Germany -- known as the P5-plus-1 because they're the five permanent U.N. Security Council members plus Germany -- would try to work out a comprehensive agreement that would end a 10-year impasse over Iran's disputed nuclear program.
The United States, Israel and other allies maintain Iran is covertly trying to develop a capacity to build nuclear weapons, a charge Tehran denies, insisting its nuclear ambitions are limited to the peaceful generation of electricity and other civilian uses.
"I don't know if we'll be able to close a deal this week or next week," Obama told a business leaders forum in Washington after meeting with the senators. "We have been very firm with the Iranians, even on the interim deal, about what we expect."
In return for Iran agreeing to several concessions, including halting advances on its nuclear program and subjecting its plants to "more vigorous inspections" than the inspections already in place, "what we would do would be to open up the spigot a little bit for a very modest amount of relief that is entirely subject to reinstatement if, in fact, they violated any part of this early agreement," Obama told The Wall Street Journal CEO Council.
The administration estimates the proposed sanctions relief would be worth $5 billion to $10 billion to Iran, a participant in the White House meeting told the Times.
During the six months of negotiations, "we could see if they could get to the end state of a position where we, the Israelis, the international community, could say with confidence Iran is not pursuing a nuclear weapon," Obama told the forum.
The most-recent three-day round of talks ended Nov. 10 after French Foreign Minister Laurent Fabius insisted the P5-plus-1 must not acknowledge Iran's right to enrich uranium and should demand Iran end construction at a plutonium-producing heavy-water reactor in Arak, a city 185 miles southwest of Tehran.
Plutonium can be used to make a nuclear bomb.
Iranian Foreign Minister Javad Zarif said during the meeting he would have to consult with Tehran on the 11th-hour changes, and the talks broke up, British newspaper The Guardian reported.
On Sunday, Zarif was quoted by the semiofficial Iranian Students News Agency as saying Tehran now saw no "necessity" for the P5-plus-1 to recognize Iran's "right" to enrich uranium -- a core demand Iran says is "non-negotiable" -- since that right is already asserted and preserved in a U.N. treaty.
Zarif said in a video posted on YouTube Tuesday the P5-plus-1 should take advantage of the "historic opportunity" to resolve the nuclear dispute.
Also Tuesday, Iranian President Hassan Rouhani spoke on the phone with British Prime Minister David Cameron, in the first direct communication between the two countries' leaders in a decade.
"Both leaders agreed that significant progress had been made in the recent Geneva negotiations and that it was important to seize the opportunity presented by the further round of talks," Cameron's office said after the call.