Lew -- whose Treasury Department is tasked with enforcing the sanctions -- was speaking yesterday at a conference in Aspen, Colorado.
"It would be the best thing for Iran and the best thing for the world if economic sanctions worked because the alternatives are worse for Iran and for the world," Lew said.
"I don't think any (US) president should make the decision about whether or not to go beyond the sanctions without having exhausted the tools available," he added.
The US treasury secretary painted a bleak picture of Iran's economy where, he said, "sanctions are working."
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"We are seeing it in Iran's GDP, we are seeing it in the value of the rial, in the employment rate, in the inflation rate. It's not a pretty picture from an economic perspective."
Lew called the current sanctions the "toughest sanctions in history," and credited an international united front: "We have not seen the kind of slippage in international support for sanctions that some people have speculated about."
"They just had an election and we are going to need to see whether this has consequences," he added, noting that such changes would "require decisions that are made at their highest level.