“They are in a state of panicked aggression,” said a senior U.S. administration official, referring to recent assaults that include attacks against energy supplies and deployment of precision-guided missiles in Lebanon and Syria. Iran denies carrying out attacks on oil tankers and Saudi infrastructure.

The key measure in the U.S. assessment is the country’s foreign-exchange reserves, representing the emergency cash that countries use to pay off trade debt, safeguard currency and stave off financial turmoil. In Iran, the currency reserves are estimated by the International Monetary Fund to be at $86 billion currently, or 20% below the level in 2013, when world-wide financial pressure forced Iran to negotiate on its nuclear program.

But the situation likely is more challenging still. Brian Hook, the U.S. State Department’s special envoy for Iran, said classified intelligence suggests Tehran has access to only 10% of those cash reserves, as sanctions against the financial sector prevent the government from tapping them.

“If Iran is going to prevent further price acceleration, then it’s going to have to burn through even more reserves,” Mr. Hook told The Wall Street Journal. “Given current sanctions on all of the top revenue-generating exports, this is simply not sustainable for the regime.”

Even if Iran has access to the full amount projected by the IMF, the fund estimates Iran will burn through another 20% next year to keep its exchange rate stable and hold down inflation, which at 36% this year is slightly higher than in 2013. Doing so would leave the central bank able to cover less than a year’s worth of imports, the projections show.

“If Iran is running dangerously low on these reserves, that could trigger a balance-of-payments crisis and a further collapse of its currency, greater hyperinflation and mass layoffs as it can’t buy the machinery and technology it needs to power its economy,” said Mark Dubowitz, chief executive of the Foundation for Defense of Democracies, a think tank that has pushed for tougher sanctions against Tehran.

Iran’s representatives at the IMF and the United Nations didn’t respond to requests for comment on the latest U.S. assessments. Mr. Rouhani acknowledged in mid-November that Washington’s oil embargo had created the most “difficult and complex conditions” since the Islamic cleric Ayatollah Ruhollah Khomeini led an armed revolt against the last shah of Iran in 1979.

U.S. officials say mismanagement and corruption are partly to blame for Iran’s economic woes, but they are exacerbated by oil and trade. The 70% fall in oil exports due to U.S. sanctions pressure reduced Iranian crude sales to an estimated 500,000 barrels a day, less than half the 2013 level of around 1.1 million barrels. Though all of Iran’s major exports fall under sanctions, enforcement has been most rigorous on crude. 

Largely because of the oil restrictions, Iran is running a trade deficit amounting to 3% of its gross domestic product. In 2013, before the start of negotiations with the U.S. and world powers, it was running a trade surplus of 7% of GDP.

All this is occurring as the country battles its deepest economic contraction in more than three decades, based on IMF data.

Normally, countries would cover a trade deficit by borrowing money, or if desperate, by tapping their foreign-currency reserves. Iran, frozen out of U.S. financial markets and struggling to access Europe’s banking system, has limited borrowing ability and is relying on its shrinking pool of reserves and cash it earns from covert sales of goods abroad.

Losing the ability to either borrow or tap its reserves could lead to a crisis requiring international intervention, such as what happened in Greece in 2010.

Mr. Hook wouldn’t specify what the U.S. assessment of Iran’s condition is based upon. The IMF’s figures for foreign-exchange reserves are an amalgamation of official Iran numbers and fund estimates, without details on how much of those reserves is actually accessible.

To be sure, Iran’s two decades of sidestepping previous U.S. and U.N. sanctions has helped Tehran master ways to help keep its economy afloat, such as oil smuggling and other tactics.

Western intelligence officials say Iran also has been able to effectively capitalize on opposition to Washington’s Iran policy in many countries, including among some European allies. A willful blindness to sanctions-busting means Tehran is able to keep cash and goods flowing, the officials said. The Europeans have set up facilities meant to evade U.S. sanctions because they believe the sanctions are bad policy.

Iran’s non-crude sales are another key lifeline. Its non-crude export revenue—largely made up of oil products such as gasoline and petrochemicals—rose to $10 billion in the three months up to July 21, up 6% compared with the same period last year, according to the Iranian customs administration.

“We have unofficial or unconventional sales, all of which are secret, because if they are made known America would immediately stop them,” Iran’s oil minister Bijan Zanganeh said in June.

Iran recently decided to cut gasoline subsidies for Iranians, in line with the new economic emphasis. It aimed to reduce consumption at home, putting more gasoline into the overseas market and plugging its budget deficit to avoid tapping shrinking cash reserves. But the move triggered mass protests from a population already at the end of its tether.

Hamid Hosseini, secretary-general of the Iran-Iraq chamber of commerce, said the reduction in domestic demand could boost Iran’s gasoline exports by 190,000 barrels a day—generating extra annual revenue of $5 billion. He said most of these supplies would likely go to Iraq and Afghanistan, which are already substantial buyers of Iran’s refined products.

Mr. Hook is skeptical that sanctions evasion and non-crude sales can overcome the U.S. sanctions campaign.

“The profound effect of U.S. sanctions cannot be offset by smuggling,” he said. “The marginal economic benefit cannot alleviate the pressure on the Iranian economy or the regime’s budget.”