Russia has managed to overcome sanctions and export controls imposed by the West to expand its missile production beyond prewar levels, according to U.S., European and Ukrainian officials, leaving Ukraine especially vulnerable to intensified attacks in the coming months.

In addition to spending more than $40 billion providing weapons for Ukraine, the United States has made curbing Russia’s military supply a key part of its strategy to support Kyiv.

As a result of the sanctions, American officials estimate that Russia was forced to dramatically slow its production of missiles and other weaponry at the start of the war in February 2022 for at least six months. But by the end of 2022, Moscow’s military industrial manufacturing began to pick up speed again, American officials who spoke on condition of anonymity to disclose the sensitive assessment now concede.

Russia subverted American export controls using its intelligence services and ministry of defense to run illicit networks of people who smuggle key components by exporting them to other countries from which they can be shipped to Russia more easily. In less than a year since the war began, Russia rebuilt trade in critical components by routing them through countries like Armenia and Turkey. U.S. and European regulators have been trying to work together to curb the export of chips to Russia, but have struggled to stop the flow to pass through countries with ties to Moscow.

Russia’s re-energized military production is especially worrisome because Moscow has used artillery to pound Ukrainian soldiers on the front lines, and its missiles to attack the electric grid and other critical infrastructure, and to terrorize civilians in cities. Officials fear that increased missile stocks could mean an especially dark and cold winter for Ukrainian citizens.

In the meantime, the Pentagon is working to find ways to help Ukrainians better take down the missiles and drones fired by Russia at civilian targets in Kyiv and military targets around the country. The Pentagon has provided Patriot air defense systems and cajoled allies to provide S-300 air defense ammunition, both of which have proven effective. It has also provided other air defenses like the Avenger system and the Hawk air defense system.

But Ukraine does not have enough air defense systems to cover the entire country, and must pick the sites it defends. An increased barrage of missiles could overwhelm the country’s air defenses, Ukrainian officials said.

In October 2022, the United States gathered international officials in Washington in an effort to strengthen sanctions on the Russian economy. At the time, American officials said they believed the sanctions and export controls were working in part because they deterred countries from sending microchips, circuit boards, computer processors and other components needed for precision guided weaponry as well as necessary components for diesel engines, helicopters and tanks.

But Russia adapted quickly with its own efforts to secure supplies of the needed parts.

Today, Russian officials have remade their economy to focus on defense production. With revenue from high energy prices, Russia’s security services and ministry of defense have been able to smuggle in the microelectronics and other Western materials required for cruise missiles and other precision guided weaponry. As a result, military production has not only recovered but surged.

Before the war, one senior Western defense official said, Russia could make 100 tanks a year; now they are producing 200.

Western officials also believe Russia is on track to manufacture two million artillery shells a year — double the amount Western intelligence services had initially estimated Russia could manufacture before the war.

As a result of the push, Russia is now producing more ammunition than the United States and Europe. Overall, Kusti Salm, a senior Estonian defense ministry official, estimated that Russia’s current ammunition production is seven times greater than that of the West.

Russia’s production costs are also far lower than the West’s, in part because Moscow is sacrificing safety and quality in its effort to build weapons more cheaply, Mr. Salm said. For instance, it costs a Western country $5,000 to $6,000 to make a 155-millimeter artillery round, whereas it costs Russia about $600 to produce a comparable 152-millimeter artillery shell, he said.

Still, Russia faces some shortcomings. It does not have huge inventories of missiles, though they have more of some kinds — like the Kh-55 air-launched cruise missile — in stock now than they did at the beginning of the war, according to people briefed on intelligence reports.

“In certain areas, they’ve been able to significantly ramp up production,” said Dmitri Alperovitch, an international security expert and chairman of Silverado Policy Accelerator, a Washington-based think tank.

In cases where Russia needs millions of one particular component, export controls can grind production to a halt. But the chips needed to make a couple of hundred cruise missiles would fit into a few backpacks, which makes evading sanctions relatively simple, Mr. Alperovitch said.

American officials said they can slow, but not stop Russia from smuggling the parts it needs for missile production and that it was unrealistic to think Moscow would not react to the American curbs. One way Russia has adapted is by shipping components to third countries then diverting them there back to Russia, according to the Commerce Department.

“Because the controls were having a real impact, the Russian government didn’t just throw up their hands and say, ‘You got us, we give up,’ ” said Matthew S. Axelrod, the Commerce Department’s assistance secretary for export enforcement. “They got more and more creative with their evasion attempts. And we have been really aggressively working a number of different ways to clamp down.”

Currently, the United States and the European Union have a joint list of 38 different categories of items whose export to Russia is restricted. American officials said nine of the 38, mostly microelectronics that power missiles and drones, are the highest priority to block.

American and European officials have been working with banks to develop a warning system to alert governments to possible sanctions violations. So far American banks have alerted the U.S. government to 400 suspicious transactions. The Commerce Department has been able to use a third of those suspicious activity reports in its investigations.

On Aug. 31, the Commerce Department accused three people of taking part in an illicit Russian procurement network. One of the three, Arthur Petrov, a Russian-German national, was arrested and charged by the Justice Department with export control violations.

Mr. Petrov is accused of acquiring microelectronics from U.S.-based exporters for the purpose of sending them to Cyprus, Latvia or Tajikistan. Once there, other companies helped send the components onward, eventually making their way to Russia.

One of the challenges for the U.S. government is that Russia does not need higher-end chips that are easier to track, but commoditized chips that can be used in a wide range of things, not just guided missiles.

“It makes our job harder because there are a lot of countries that it’s legal and totally fine to sell those chips to for legitimate commercial purposes,” Mr. Axelrod said. “The problem is when those chips then get diverted and shipped to Russia.”

American and Western officials say there is some good news. Russian production is still not keeping pace with how fast the military is burning through ammunition and wearing out equipment. For example, even though Russia is on pace to produce two million rounds of ammunition a year, it is firing more than 10 million rounds of artillery at the same time. That has led Moscow to desperately search for alternative sources to increase its stocks, most recently by trying to secure a weapons deal with North Korea, American and Western officials said.

And although Moscow has been successful in smuggling processors and circuit boards, it is facing a shortage of rocket propellant and basic explosives, American officials said, material that can be harder to smuggle than circuit boards. Those shortages are likely to constrain Moscow if it tries to step up further production of ammunition, missile or bomb.

Russa’s increased military production has also come at a great cost to the Russian economy, particularly as interest rates spike in the country. Sanctions have taken a toll on the Russian economy’s overall health, and overcoming Western export bans has not come cheaply, said American and Western officials. The senior Western defense official said that Russia had reallocated nearly a third of its commercial economy toward arms production. The country faces a labor shortage that could make further industrial gains harder to achieve too.

Russia cut back on its attacks on Ukraine’s energy grid during the summer. But as temperatures plunge, some Ukrainian and Western analysts and government officials think Russia could renew the terror campaign on Kyiv, in hopes that it will sap Ukrainians’ will to fight.

U.S. officials hope the steady supply of air defense ammunition and additional help to improve how Ukraine intercepts Russian attacks could help counter a reinforced barrage of missiles. And Ukrainian defenses have — in some situations — grown stronger.

“Ukrainians have become better in defending their infrastructure and building defenses around their power stations and critical power grids,” Mr. Salm said. “They have become better at fixing and making sure that the impact of the power outages and other utility outages are not as harsh.”