WASHINGTON — The United States, in partnership with its allies, has hit Russia with some of the most sweeping export restrictions ever imposed, barring companies across the world from sending advanced technology in order to penalize President Vladimir V. Putin for his invasion of Ukraine.

The restrictions are aimed at cutting off the flow of semiconductors, aircraft components and other technologies that are crucial to Russia’s defense, maritime and aerospace industries, in a bid to cripple Mr. Putin’s ability to wage war. But the extent to which the measures actually hinder Russia’s capabilities will depend on whether companies around the globe follow the rules.

Enforcing the new restrictions poses a significant challenge as governments try to police thousands of companies around the world. But the task could be made easier because the United States is acting in concert with so many other countries.

The member states of the European Union, Japan, Australia, Canada, New Zealand, the United Kingdom and South Korea have joined the United States in imposing their own restrictions. And governments including Singapore and Taiwan, a major global producer of semiconductors, have indicated they will support the rules.

“Because we have the full cooperation and alignment with so many countries, it makes enforcement a lot easier,” Gina Raimondo, the U.S. secretary of commerce, said in an interview. “Every country is going to be doing enforcement.”

“That’s part of the power, if you will, of having so much collaboration,” she added.

Officials from the Commerce Department, which is in charge of enforcing the U.S. rules, have already begun digging through shipping containers and detaining electronics, aircraft parts and other goods that are destined for Russia. On March 2, federal agents detained two speedboats at the Port of Charleston valued at $150,000 that were being exported to Russia, according to senior U.S. officials.

To look for any potential violators, federal agents will be combing through tips from industry sources and working with Customs and Border Protection to find anomalies in export data that might point to shipments to Russia. They are also reaching out to known exporters to Russia to get them on board with the new restrictions, speaking to about 20 or 30 companies a day, U.S. officials said.

Their efforts extend beyond U.S. borders. On March 3, Commerce officials spoke to a gathering of 300 business people in Beijing about how to comply with the new restrictions. U.S. officials have also been coordinating with other governments to ensure that they are taking a tough stance on enforcement, senior U.S. officials said.

Emily Kilcrease, director of the energy, economics and security Program at the Center for a New American Security, said that the level of allied cooperation in forging the export controls had been “completely unprecedented,” and that international coordination would have an important upside.

“The allied countries will be active partners in enforcement efforts, rather than the United States attempting to enforce its own unilateral rules extraterritorially,” she said.

It remains to be seen how effective the rules are in degrading Russian military capability or dissuading its aggression against Ukraine. But in their initial form, the broad scope of the measures looks like a victory for the multilateralism that President Biden promised to restore.

Mr. Biden came into office pledging to mend ties with Europe and other allies that had been alienated by former President Donald J. Trump’s “America first” approach. A key part of the argument was that the United States could exert more pressure on countries like China when it was not acting alone.

That approach has been particularly important for export controls, which experts argue can do more harm than good when they are imposed by only one country — a criticism that was sometimes leveled at the export controls the Trump administration issued on China.

The Russian invasion of Ukraine has unified Western governments like few issues before. But even with countries eager to penalize Russia, coordinating restrictions on a vast array of complex technologies among more than 30 governments was not simple. The Commerce Department held more than 50 discussions with officials from other countries between the end of January and Feb. 24, when the controls were announced, as they hashed out the details, senior U.S. officials said.

Much of that effort fell to Matthew S. Borman, a three-decade employee of the Commerce Department, who in late January began near-daily conversations with the European Commission and other countries.

In mid-February, Mr. Borman and a senior aerospace engineer flew to Brussels for meetings with Peter Sandler, the European director general of trade, and other staff. As a “freedom convoy” protesting coronavirus restrictions attempted to roll into Brussels, they worked from early in the morning until late in the night amid reams of paper and spreadsheets of complex technological descriptions.

Each country had its own byzantine regulations, and its own interests, to consider. The European Commission had to consult its 27 member countries, especially tech powers like Germany, France, the Netherlands and Finland, on which products could be cut off. Officials debated whether to crack down on the Russian oil industry, at a time of soaring gas prices and inflation.

As Russia’s neighbor, the Europeans wanted to ensure Russia could still access certain goods for public safety, like nuclear reactor components to avoid a Chernobyl-style meltdown. At least one foreign country insisted that auto exports to Russia should continue, a senior administration official said.

The breakthrough came when American officials offered a compromise. The Biden administration planned to issue a rule that would bar companies anywhere around the world, even outside of the United States, from exporting certain products to Russia if they were made using American technology. But those measures would not apply in countries that joined the United States and Europe in issuing their own technological restrictions on Russia.

In an interview, Mr. Borman said that American allies had historically been concerned with the extraterritorial reach of U.S. export controls, and that the exclusions for countries that imposed their own rules “was really the key piece.”

“We all realized that at a strategic level what was most important was to have a unified allied position,” he said.

The rules now prevent companies around the world from sending Russia high-tech goods like chips, telecommunications items and navigation equipment. They are even tougher for certain entities with ties to the Russian military, which cannot import so much as a pencil or toothbrush.

Ms. Raimondo said the impact of the measures would likely be felt over a period of months, rather than weeks, as Russian tanks and aircraft are destroyed, and the controls prevent the Russian military from obtaining materials to fix them. Over time, she said, the restrictions should prove “very disabling to their military.”

While some companies may want to continue supplying parts to Russia in violation of those rules, there are powerful incentives against doing so, U.S. officials said, including the detention of goods, fines and even jail time.

The Commerce Department currently has 130 federal agents working in 30 cities in the United States to check for violators, as well as nine employees overseas. It expects to add personnel in Europe and Asia to carry out more expansive checks, officials said.

Kevin Wolf, an international trade partner at Akin Gump and a former Commerce department official, said that implementing the policy was likely to be “extraordinarily complex,” but that it would immediately alter company behavior.

“Even if they’re not perfect, I still think you will see a significant reaction by multinationals to do everything they can to comply,” Mr. Wolf said.

“Just because people speed doesn’t mean you don’t have a speeding limit,” he added.

One potential focus is China, which has expressed a worrying allegiance with Russia. But Chinese leaders have also hinted that they will comply with the sanctions to protect their own economic interests.

Ms. Raimondo has warned that the United States could take “devastating” action against Chinese companies that violate the policy, cutting them off from the U.S. technology and equipment necessary to make their products.

“They have their own self-interest to not supply this stuff to Russia,” she added.

On Monday, Jake Sullivan, the national security adviser, met with Chinese foreign affairs official Yang Jiechi in Rome to discuss reports that Russia had asked China for economic and military assistance for its war in Ukraine.

China has denied those reports. Jen Psaki, the White House press secretary, said Monday that she was not able to confirm any intelligence, but that Mr. Sullivan had conveyed that if China provided military or other assistance that violated sanctions or supported the war effort “there will be significant consequences.”

“But in terms of what the specifics look like, we would coordinate with our partners and allies to make that determination,” she added.