Iraqis are blaming an unexpected culprit for a weakening currency that has caused the price of food and imported goods to rise: a little-noticed policy change by the U.S. Treasury and the Federal Reserve Bank of New York.

The New York Fed began enforcing tighter controls on international dollar transactions by commercial Iraqi banks in November in a move to curtail money laundering and the illegal siphoning of dollars to Iran and other heavily sanctioned Middle East countries, U.S. and Iraqi officials said.

Iraqi banks had operated under less stringent rules since shortly after the 2003 U.S. invasion that toppled Saddam Hussein. But years of weak governments and crises—from the insurgency during the U.S. occupation to the Islamic State takeover of large portions of the country—led successive administrations to put off bringing Iraq’s banking system into compliance with global money-transfer practices until now, officials said.

Since the procedures went into effect, 80% or more of Iraq’s daily dollar wire transfers, which previously totaled over $250 million some days, have been blocked because of insufficient information about the funds’ destinations or other errors, according to U.S. and Iraqi officials and official Iraqi government data.

With dollars scarce, Iraq’s currency has fallen as much as 10% against the dollar, leading to sharply higher prices for imported goods, including staples such as eggs, flour and cooking oil.

“For 20 years we followed the same system,” said Mahmood Daghir, chairman of Al Janoob Islamic Bank and a former Central Bank of Iraq official. “But the shock policy by the Fed has made a crisis inside the Iraqi economy.”

The turmoil exemplifies the wary but interwoven relationship between Washington and Baghdad. Since the U.S. helped establish the Central Bank of Iraq in 2004, the U.S. dollar has largely become the country’s chief currency because so much of the economy runs on cash.

To keep Iraq supplied with dollars, planes deliver pallets of U.S. currency to Baghdad every few months. But far more dollars flow electronically in transactions by Iraq’s private banks, processed from Iraq’s official accounts at the New York Fed where proceeds from its oil sales are deposited.

U.S. officials say the tighter rules for electronic dollar transfers by Iraqi private banks weren’t a surprise to officials in Baghdad. They were implemented jointly in November after two years of discussions and planning by the Central Bank of Iraq, the U.S. Treasury and the Fed. The rise in the dollar exchange rate wasn’t caused by the new measures, the U.S. officials added.

But the scrutiny of dollar transactions has set off a rush for greenbacks in Iraq and a torrent of criticism from Iraqi officials, bankers and importers who blame the new system for an unnecessary financial jolt that has worsened their already severe economic woes.

Iraqi Prime Minister Mohammed al Sudani, who took office just as the currency began to drop, said the Fed’s action was harming the poor and threatening his government’s 2023 budget.

“This is embarrassing and critical for me,” he said in an interview. He said that he would send a delegation to Washington next month with a proposal for a six-month moratorium on the new policy.

Some senior Iraqi officials with ties to Iran have been even more critical. “Everyone knows how the Americans use the currency as a weapon to starve people,” Hadi al-Amiri, the head of an Iranian-backed political party and militia, told the French ambassador in a Jan. 10 meeting, according to an account released by Mr. Amiri’s office.

Under the new procedures, Iraqi banks have to submit dollar transfers on a new online platform with the central bank, which are then reviewed by the Fed.

The system is aimed at curtailing use of Iraq’s banking system to smuggle dollars to Tehran, Damascus and money laundering havens across the Middle East, U.S. officials said.

Under the old rules, Iraqi account holders weren’t required to disclose to whom they were sending money until after the dollars had already been transferred, said Mr. Daghir, the former central bank official.

A spokeswoman for the New York Fed said of accounts it maintains for foreign governments, such as Iraq’s, “We have a robust compliance regime for these accounts that evolves over time in response to new information.”

A U.S. official said the measures would limit “the ability of malign actors to use the Iraqi banking system.”

The U.S. Treasury and the Central Bank of Iraq declined to comment. The Iraqi central bank described the new electronic platform in a Dec. 15 statement that said it required “full details of customers who want money transfers,” including final beneficiaries.

“A number of mistakes are being discovered and banks are required to redo the process,” the statement said. “Such procedures will take additional time before getting accepted and passed by the international system.”

The central bank also barred four banks—Islamic Asia Bank, Iraqi Middle East Bank, Ansari Islamic Bank and Al Qabudh Islamic Bank—from carrying out any dollar transactions, according to Iraqi officials and court documents. Executives at Asia Bank and Ansari Bank declined to comment, while the two other institutions couldn’t be reached.

U.S. officials have pressed Iraq for years to strengthen its banking controls. In 2015, the Federal Reserve and Treasury Department temporarily shut off the flow of billions of dollars to Iraq’s central bank over concerns that the currency was ending up at Iranian banks and possibly being funneled to Islamic State militants, officials said at the time.

Some Iraqi officials supported tougher scrutiny of private banks. Hadi al Salami, a member of Iraq’s Parliament who serves on the body’s anticorruption commission, said Iraq’s political parties and militias control most of the banks, using them to smuggle dollars to neighboring countries. “We need this to be stopped immediately,” he said.

The impact of the tighter controls adopted in November can be seen in the steep decline in Iraqi banks’ dollar transactions, which the central bank tracks on its website. On Oct. 17 last year, before the new rules went into effect, the daily transfer from Iraq’s official accounts at the New York Fed and other overseas institutions was $224.4 million, according to the data. On Jan. 17, it was $22.9 million, a drop of nearly 90%.

U.S. officials say the financial turmoil will ease as Iraqi account holders comply with disclosure requirements.

Even Iraqi bankers and currency traders say the stricter rules are aimed at shutting down schemes used to siphon dollars. For instance, they say, importers falsify invoices for goods that are never delivered to Iraq but paid for in dollars flowing to unknown recipients outside the country.

“The dollars in Iraq, for sure 100%, are going to Iran, Turkey, Syria, Yemen, Lebanon and sometimes Dubai,” said Hamza al Sarraf, sitting behind the barred counter of his currency exchange shop in Baghdad’s bustling Karada neighborhood.

The clampdown on electronic dollar transfers has sparked a frenzy for paper dollars in exchange shops and bigger currency-trading houses, Mr. Sarraf said, checking the informal dollar exchange rate in Baghdad on his smartphone.

Blocked from using banks, Iraqi importers have had to delay orders while they work to comply with the new rules or find other methods to pay suppliers, such as using informal money-transfer networks known as hawala. Some traders, Mr. Sarraf said, are loading up on dollars and shipping them out of Iraq in vehicles.

The official exchange rate is fixed at 1,470 Iraqi dinars to the dollar. But at Baghdad banks and exchange houses, the dollar was selling for as high as 1,620 Iraqi dinars on Tuesday, as much as 10% higher than last November, according to data released by the Central Bank of Iraq.

As the dollar has gained in value, it has cut into sales of imported items, said Ghaith al Badry, who owns a small cellphone shop in Baghdad.

A Samsung smartphone that he buys in dollars in Dubai and sold for 200,000 dinars in November is now 219,000 dinars, he said. With food prices also going up, Mr. Badry said, his customers have disappeared.

“No one is buying mobile phones,” he said in his empty shop. “They’re worrying about food.”

Corrections & Amplifications

U.S. currency deliveries to Baghdad are made on aircraft arranged by the Iraqi government. An earlier version of this article incorrectly said that the currency deliveries are made on U.S. Air Force planes. (Corrected on Jan. 19)

Ghassan Adnan contributed to this article.

WSJ by David S. Cloud