By Jay Solomon And William Mauldin 

WASHINGTON--Iran's economy is now "fundamentally" incapable of recovery without a nuclear accommodation with the West, increasing Washington's leverage in final negotiations with Tehran, said the Treasury Department's outgoing sanctions czar David Cohen.

"They're stuck. They can't fix this economy unless they get sanctions relief," Mr. Cohen said in an interview with The Wall Street Journal about sanctions policy around the world. "I think they are coming to the negotiations with their backs to the wall."

Mr. Cohen is leaving his post to assume the No. 2 spot at the Central Intelligence Agency next month, where he'll continue to spearhead U.S. efforts to contain Iran, Russia, North Korea and other American adversaries. Mr. Cohen has been a central player at Treasury over the past decade in developing targeted financial sanctions to pressure countries and extremist organizations, such as Islamic State.

In Washington, many see Mr. Cohen's rise to the post of deputy CIA director as underscoring the importance the White House now assigns to financial intelligence.

"I think it would be accurate to say that the importance of financial tools in our national security toolbox has steadily increased over the past five to 10 years," Mr. Cohen said. "Had that not been the case...I would have never gotten on the radar screen of somebody like John Brennan," the CIA's director.

The administrations of Barack Obama and George W. Bush have both touted the U.S. financial campaign against Iran as a model for weakening Washington's adversaries. Mr. Cohen and other senior U.S. officials say they believe that Tehran's decision in 2013 to negotiate over its nuclear program resulted from the sanctions damage to the economy.

The Treasury Department calculates the Western sanctions have cut Iran's oil exports by more than half in three years, while denying Tehran $40 billion in revenues last year alone. Recent declines in oil prices, according to Mr. Cohen, could cost Iran another $11 billion over the next six months.

Republican and Democratic critics of the White House still accuse the U.S. of not going far enough. A bi-partisan bill now being negotiated in Congress would call for new sanctions against Iran if an international agreement curbing its nuclear program isn't reached by July.

Some critics also maintain the administration relies too heavily on sanctions alone, without a broader policy of addressing global problems.

"Sanctions are not the policy and they should not serve as a cover-up for a lack of policy," said Slovakia's foreign minister, Miroslav Lajcak, in an interview. Mr. Lajcak, whose country has suffered fallout from the sanctions against Russia, says he doesn't question the need for economic penalties, but also favors greater support for his neighbor, Ukraine.

Some economic analysts disagree with Mr. Cohen, saying the decision by the White House last year to suspend some sanctions to advance the diplomacy has breathed new life into the Iranian economy.

"Iran's new budget shows that the authorities see no urgent need for relief from the current sanctions," Patrick Clawson of the Washington Institute for Near East Policy, told a congressional hearing this week. "They correctly feel that they have learned to live with those sanctions."

Mr. Cohen said that imposing new sanctions on Iran now could destroy the international coalition imposing them. He voiced skepticism that escalating sanctions alone, without diplomacy, could cause Tehran to capitulate on the nuclear issue.

"Who knows what would have happened had we continued on with sanctions, whether they would have careened to disaster," Mr. Cohen said. "I think that's unknowable."

Targeted sanctions in response to Russian President Vladimir Putin's Ukraine incursion have contributed to a 50% drop in the value of Russian ruble over the past six months and slashing of economic growth forecasts.

Anders Aslund of the Peterson Institute of International Economics said Russian output could tumble 10% this year. Last week, Standard & Poor's Ratings Services cuts its credit rating on Russia to junk-level.

Mr. Cohen also said the U.S. and its allies have made gains in cutting off the financing of Islamic State fighters in Iraq and Syria. Pentagon warplanes have destroyed much of the organization's oil infrastructure, used by the organization for income and donations for the group from Persian Gulf sympathizers also have diminished under U.S. pressure, according to U.S. officials.

Still, Mr. Cohen said Islamic State, which is also known as ISIS or ISIL, continues to earn revenues from crime and kidnapping.

"We don't pay ransoms to hostage-takers, especially not to terrorist organizations that are hostage-takes," Mr. Cohen said, without commenting on current hostage dramas. "ISIL gets a material amount of its funding from ransom payments. And it would be to all of our mutual benefit to cut off that source of funding."