WASHINGTON — Using a mix of high-tech and Cold War tactics, Ukrainian activists and Western institutions have begun to pierce the propaganda bubble in Russia, circulating information about the Ukraine war among Russian citizens to sow doubt about the Kremlin’s accounts.

The efforts come at a particularly urgent moment: Moscow appears to be preparing for a new assault in eastern Ukraine that could prove devastatingly bloody to both sides, while mounting reports of atrocities make plain the brutality of the Kremlin’s tactics.

As Russia presents a sanitized version of the war, Ukrainian activists have been sending messages highlighting government corruption and incompetence in an effort to undermine faith in the Kremlin.

Radio Free Europe/Radio Liberty, a U.S.-funded but independent news organization founded decades ago, is trying to push its broadcasts deeper into Russia. Its Russian-language articles are published on copies of its websites called “mirrors,” which Russian censors seek out in a high-stakes game of whack-a-mole. Audience numbers have surged during the war despite the censorship.

American organizations are also promoting the use of software that allows Russian citizens to leap over the nascent firewall erected by the Kremlin to control internet access.

The efforts face high barriers as the Kremlin tightens controls on journalists and the internet, passing laws that have forced the closure of independent media outlets, like the Echo of Moscow. President Vladimir V. Putin is doing all he can to keep Russians in the dark about Europe’s largest land war since 1945, with casualties going largely unreported in Russian news media.

The Russian government has focused in particular on restricting reports of war casualties. In its most recent official announcement, in late March, Russia reported 1,351 military deaths, while the latest American intelligence estimate, which was shared with Congress in recent days, put the number at 4,000 to 5,000.

But cracks in Moscow’s facade are starting to show. On Thursday, the Kremlin’s spokesman acknowledged that Russia had suffered “significant losses.”

After the war started in February, Mr. Putin began erecting an internet firewall similar to China’s to block some Russian and Western news sites and social media networks. Russians can still visit Google and YouTube, but many Western sources of news are labeled “foreign agents.”

An authoritarian government does not have to maintain a perfect firewall to keep its public in a propaganda bubble. Many Russians get their news from state-controlled television and radio. And some Russian analysts argue that most citizens support the government for reasons beyond their news diet and want to believe the Kremlin’s lines.

American intelligence officials say that is why pushing information into Russia, and reaching the broadest population, is so difficult.

Nevertheless, American and European officials say that the attempt by outsiders to get facts about the war to Russians is important.

For now, Mr. Putin and the invasion remain popular in Russia, according to polls, though analysts caution that such measures of Russian attitudes are unreliable, mainly because many people fear making antiwar statements. The police have arrested thousands of protesters, and many people self-censor their remarks on Ukraine.

There are early signs that the efforts to break down the wall of propaganda may be working, said a senior Western intelligence official, who like other security officials spoke on the condition of anonymity to discuss classified or sensitive government assessments.

And an American data analytics company, FilterLabs.AI, which has been tracking Russian sentiment on internet message boards and other online forums, says it has measured growing anxiety among Russians about the draft and war casualties. Mr. Putin recently signed a decree ordering up about 134,500 conscripts, though the Defense Ministry said they would not go to Ukraine.

“We could be at a turning point in Russian sentiment toward the initial invasion of Ukraine, when Russia attempted to take over the whole country,” said Jonathan D. Teubner, the chief executive of FilterLabs.

Planting the Seeds of Doubt

The email to the 18-year-old Russian was, in some ways, subtle. It did not directly mention the invasion of Ukraine or allegations of war crimes against Russian soldiers.

Instead, it talked about the mistreatment of Russian soldiers by their own military and suggested the Russian government was lying to conscripts and, crucially, providing inadequate food and equipment to the country’s soldiers.

Over the last two weeks, a group of Ukrainian activists, government officials and think tanks, called the Information Strategies Council of Ukraine, has sent emails and social media messages to 15 million Russian men of draft age, between 18 and 27. It aimed other posts at older Russians, using historical references to prod them to discuss government-sanctioned news reports.

“The fundamental problem is that when you want to tackle the propaganda, you cannot just say what you are getting on TV is not true; it doesn’t work like that,” said Sophia Hnizdovska, an executive at the council. “We are trying to slowly, through our narratives, make people question the official sources.”

The most successful posts by the Ukrainian activists have built on this theme, focusing on the incompetence and corruption of Russian military leaders, members of the group say.

One image circulated by the group portrayed senior Russian military leaders, including Sergei K. Shoigu, the defense minister, with his head filled with question marks and Gen. Valery Gerasimov, the senior military leader, with his head filled with an image of a superyacht.

Russians tend to dismiss messages highlighting Russian war crimes as American propaganda, according to activists, and pictures of Russian casualties run the risk of inciting anger at Ukraine, rather than the Kremlin.

Mr. Teubner’s company is trying to measure the Ukrainians’ success — and in recent days has tracked what appears to be growing negative sentiment across Russia toward a draft. If the Ukrainians can sow enough doubt about the truthfulness of the Russian government, Ms. Hnizdovska said, more Russians will seek out information from Western-supported Russian-language news media.

Radio Waves and Real News

During the Cold War, the U.S. government, and the C.I.A. specifically, helped found and fund independent media organizations with the mission to penetrate the Iron Curtain with fact-based news.

With the invasion of Ukraine, the organizations are once again operating with a sense of urgency as they push to get accurate information inside an authoritarian state.

The news organizations are using both old-school and 21st-century tactics, creating radio programs and complex digital information campaigns.

Radio Free Europe/Radio Liberty, the main private, independent news organization in the region with U.S. government financing, is producing journalism on the war from reporters on the front lines in Ukraine and working quietly in Russia.

Commonly known as RFE/RL, the group has a Russian-language news site and a 24-hour Russian-language television network, Current Time, as well as websites aimed at regional audiences in a wide range of languages, including Tatar, Chechen and Belarusian.

Like some other news organizations and U.S.-based social media companies, its websites were blocked in Russia starting in late February. And it suspended its main operations in Russia last month.

RFE/RL opened offices in Lithuania and Latvia as new bases for its reporting on Russia. The group also has a medium-wave radio transmitter in Lithuania to send broadcasts into Russia that can be picked up on an AM frequency. Officials said they hoped to expand the signal’s strength.

The group uses Telegram, a chat app, to disseminate some of its reporting and to send out the web addresses of its new “mirror” sites.

A Washington-based sister organization that also gets funding from the U.S. government, the Open Technology Fund, sets up the mirror sites and constantly creates new ones to stay a step ahead of Russian government censors.

“In the context of new censorship, the mirror program has grown rapidly and Russian censors are proving to be a very active adversary,” said Nat Kretchun, the organization’s senior vice president for programs. “Our partners are setting up a more automated system where once the Russian censors block them, new sites are set up.”

The technology group arranges for some of Radio Free Europe/Radio Liberty’s sites to be hosted by Tor, a digital communications network that helps shield ordinary internet users from surveillance. And it gives financing to companies and groups developing virtual private network apps, software known as VPNs, that help citizens get around internet firewalls. Owners of smart TVs in Russia can also download an app for Current Time.

And Current Time is among the RFE/RL networks and programs with channels on YouTube, which, unlike Facebook and Instagram, has not been blocked by Russian censors. RFE/RL said the number of video views on its YouTube channels more than tripled in the first three weeks of the war, to 237.6 million, from the three weeks prior.

“We’re seeing higher audience numbers for Russians inside the country and also for Russians outside,” said Jamie Fly, the president and chief executive of RFE/RL. “The challenge is: Can we maintain that over time? Will interest fade?”

In mid-March, Russian news outlets began running stories saying that Russian casualties in Ukraine were low, in contrast to much higher Western estimates. Those reports, according to an analysis by FilterLabs, came just as concern about the country’s war dead was starting to rise on local internet message boards — and as soldiers’ coffins began returning home.

Stories about Russian soldiers killed in Ukraine and Russian prisoners of war are among the most popular across RFE/RL platforms, said Patrick Boehler, the head of digital strategy for the news organization. The news agency’s reporters in Ukraine who learn the identities of Russians killed or taken prisoner pass that information to colleagues in Russia, who then try to find and interview the families.

The software developed by FilterLabs began tracking changes in public sentiment and shifts in how Russian news outlets talk about wartime casualties. Some skeptics question this kind of artificial-intelligence-driven sentiment analysis, and FilterLabs acknowledges that the technology has limits.

But the group says the broad trends it identifies are reliable and show that concern about the draft is increasing, as discussions on message boards appear to indicate that Russians are growing more worried that their children will be conscripted into the military to fight in Ukraine, Mr. Teubner said.

“The overall sentiment when talking about the draft is trending very negatively in the popular forums,” he said. “This shows us what is likely one of the greatest vulnerabilities for those trying to maintain support for the war over the long term.”