New penalties would not kick in for several months, Corker said, and the current sanctions could be toned down, if necessary, based on Iran's actions.
He said: "I think this week sitting down, talking with Secretary Kerry is going to be an important element of what we do. ... We know the sanctions have gotten us here, and we're worried we're dealing away with our leverage."
Sen. Bob Menendez (D-N.J.), chairman of the Senate Foreign Relations Committee who has repeatedly sponsored tough sanctions legislation, spoke of "the possibility of moving ahead with new sanctions, including wording it in such a way that if there is a deal that is acceptable, that those sanctions could cease upon such a deal."
He said on the
that "it's an insurance for the United States to make sure that Iran actually complies with an agreement that we would want to see."
At the same time, he said, it would be an incentive for the Iranians "to know what's coming if you don't strike a deal."
Sen. Lindsey Graham (R-S.C.) said sanctions have brought Iran to the negotiating table and "if we back off now, I think that's exactly the wrong signal."
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that "a new round of sanctions will be coming from the Congress. The Congress will define the end game because we're worried about the end game, not some interim deal. You can't trust the Iranians."
In the broader region, he said, "the Israelis are apoplectic about what we're doing. I've never been more worried about the Obama administration's approach to the Mideast then I am now."
A top Kerry deputy, Wendy Sherman, arrived Sunday in Jerusalem for a one-day visit for consultations on Iran, the State Department said.
President Barack Obama has said that if Iran halts advances and reverses parts of its nuclear program, the United States would offer "modest relief" to ease the economic squeeze on Tehran.
But he told
in an interview last week that core sanctions would remain and that if Iran's leaders back out of a deal "we can crank that dial back up." Such measures include penalties that have crippled Tehran's oil exports.