The intense pressure of international sanctions, led by the United States, brought the Iranian government to the negotiating table in Geneva, where, on Nov. 24, the six major powers and Iran agreed to a Joint Plan of Action on Iran's nuclear program. As the principal U.S. official charged with crafting and enforcing our sanctions program, I am confident that the sanctions pressure on Iran will continue to mount. Iran will be even deeper in the hole six months from now, when the deal expires, than it is today.

Here's why.

To begin with, the relief package in this interim deal is economically insignificant to Iran. The lion's share of the relief comes from granting Iran access, in installments, to $4.2 billion of its own revenues currently trapped outside Iran. In addition, U.S. sanctions on Iran's petrochemical exports and its auto industry will be temporarily suspended.

We estimate that this additional trade could generate about $1.5 billion in revenue over the next six months—but only if Iran is able to find customers to buy its cars and petrochemical products. This will be difficult: There are long-standing problems with Iran's auto sector, and petrochemical importers prefer long-term contracts, which aren't possible given the six-month duration of the deal.

The Joint Plan also suspends sanctions on Iran's ability to buy and sell gold. But because remaining prohibitions preclude Iran from using either its foreign reserves or its own currency to buy gold, this provision is of limited value. Any gold Iran purchases would be offset by the hard currency it would spend to buy it.

Under strict guidelines, the deal also allows Iran to transfer $400 million of restricted Iranian funds to defray tuition costs for Iranian students studying abroad.

If the Iranians comply with their obligations under the Joint Plan, over the next six months they will stand to receive $6 billion to $7 billion in relief, mostly by gaining access to their own money. Not $1 comes from U.S. taxpayers.

Viewed in light of Iran's struggling economy, this sum is inconsequential. Iran is in a deep recession—its economy contracted last year by more than 5%, and it is on pace to contract again this year. Its annual inflation rate now stands at about 40%. Iran's currency, the rial, has lost around 60% of its value against the dollar since 2011.

The total relief is a small fraction of the roughly $80 billion Iran has lost since early 2012 because of U.S. and European Union oil sanctions, and of the nearly $100 billion in Iran's foreign-exchange holdings that are mostly restricted or inaccessible due to U.S. financial and banking sanctions.

Iran's economy will also continue to suffer because the core architecture of U.S. sanctions—especially our potent oil, financial and banking sanctions—remains firmly in place. The oil sanctions alone cost Iran about $5 billion a month in lost sales, meaning that over the six-month duration of the Joint Plan, Iran will lose about $30 billion in oil revenue. Iran's access to whatever oil revenue it earns, moreover, won't be available for transfer or repatriation.

All of our sanctions against major Iranian financial institutions also remain in place, which means that Iran will remain largely cut off from the international banking system, curbing its ability to move or spend its cash. The sanctions that forbid investment in Iran's energy sector, including helping to develop Iran's oil and natural gas resources, remain in place, as does the long-standing comprehensive ban on U.S. business with Iran.

As President Obama said when he announced the Joint Plan, we are fully committed to vigorous enforcement of these sanctions. We know that sanctions do not implement themselves. To disrupt and disable those facilitating Iran's nuclear and missile programs, we will identify front companies, evaders and malefactors and sanction them. Along with our partners across the U.S. government, my team at Treasury has done so more than 600 times in the last several years. This will continue unabated.

To maintain pressure on Iran's economy, we will continue to present foreign banks with a stark choice: They can either do business with designated Iranian banks and businesses, or they can do business with the U.S.—not both. To keep Iran's oil revenues depressed, we will ensure that Iran will not be able to export one additional barrel beyond the current low levels. And to hold back latent interest in trade with Iran, we will communicate a blunt message to every foreign official, businessperson and banker who thinks now might be a good time to test the waters: We are watching, and we are poised to act against anyone, anywhere, who violates our sanctions.

Sanctions gave Iran a powerful incentive to accept this first-step deal, and they will be key to negotiating the comprehensive resolution that ensures Iran cannot obtain a nuclear weapon. Now is no time to let up—and we won't.

Mr. Cohen is the undersecretary for terrorism and financial intelligence at the Treasury Department.