Since Russia invaded Ukraine, Defense Secretary Lloyd J. Austin III has rarely spoken to his Russian counterpart. Credit…Kenny Holston/The New York Times

Earlier this month, Defense Secretary Lloyd J. Austin III received an unusual request from an unlikely caller: His Russian counterpart wanted to talk.

Since Russia invaded Ukraine in February 2022, Mr. Austin had spoken by phone with Russia’s defense minister only five other times, almost always at the Pentagon’s initiative and often in an effort to avoid miscalculations that could escalate the conflict.

In fact, Mr. Austin had reached out to Russia’s new defense minister, Andrei Belousov, just a couple of weeks earlier, on June 25, in an effort to keep the “lines of communication open,” the Pentagon said. It was the first phone call between the two men since Mr. Belousov, an economist, replaced Sergei K. Shoigu, Russia’s long-running defense minister, in a Kremlin shake-up in May.

Now on July 12, Mr. Belousov was calling to relay a warning, according to two U.S. officials and another official briefed on the call: The Russians had detected a Ukrainian covert operation in the works against Russia that they believed had the Americans’ blessing. Was the Pentagon aware of the plot, Mr. Belousov asked Mr. Austin, and its potential to ratchet up tensions between Moscow and Washington?

Pentagon officials were surprised by the allegation and unaware of any such plot, the two U.S. officials said, speaking on the condition of anonymity to discuss the confidential phone call. But whatever Mr. Belousov revealed, all three officials said, it was taken seriously enough that the Americans contacted the Ukrainians and said, essentially, if you’re thinking about doing something like this, don’t.

Despite Ukraine’s deep dependence on the United States for military, intelligence and diplomatic support, Ukrainian officials are not always transparent with their American counterparts about their military operations, especially those against Russian targets behind enemy lines. These operations have frustrated U.S. officials, who believe that they have not measurably improved Ukraine’s position on the battlefield but have risked alienating European allies and widening the war.

Over the past two years, the operations that have unnerved the United States included a strike on a Russian air base on the western coast of Crimea, a truck bombing that destroyed part of the Kerch Strait Bridge, which links Russia to Crimea, and drone strikes deep inside Russia.

President Vladimir V. Putin of Russia often refers to such strikes as “terrorist attacks,” and the Kremlin uses them as evidence to back up Mr. Putin’s spurious claim that his invasion of Ukraine is really a defensive war. Despite American denials, Russian officials insist publicly that such strikes could not happen without U.S. approval and support.

Whether the alleged Ukrainian plot this month was real and imminent is still unclear, as is what form it might have taken. Pentagon and White House officials say nothing has happened — yet. They have declined to describe the call in detail but stressed the need for dialogue among adversaries.

“During the call, the secretary emphasized the importance of maintaining lines of communication amid Russia’s ongoing war against Ukraine,” Sabrina Singh, a Pentagon spokeswoman, told reporters hours after the conversation on July 12.

Pentagon officials declined to say if Mr. Austin brought up the matter in a phone call on Tuesday with his Ukrainian counterpart, Rustem Umerov.

A Russian Defense Ministry statement after the July 12 call confirmed that Mr. Belousov initiated it, adding that “the issue of preventing security threats and reducing the risk of possible escalation was discussed.” But the statement made no mention of a suspected Ukrainian covert mission.

Ukrainian officials declined to comment on the matter. The Kremlin also declined to comment for this article, and the Russian Defense Ministry did not respond to a request for comment.

The rare glimpse behind the scenes of a sensitive call between defense ministers illustrates how much more there often is to private conversations between American and Russian officials than what is revealed to the public. And how the United States and Russia try to manage escalation risks behind the scenes.

Mr. Austin and Mr. Belousov “exchanged views on the situation around Ukraine,” the Russian Defense Ministry said in a statement about the same call. It added that Mr. Belousov “pointed to the danger of further escalation of the situation in connection with the continued supply of American weapons to the Armed Forces of Ukraine.”

But two officials familiar with the call said Mr. Austin also warned his Russian counterpart not to threaten U.S. troops in Europe amid rising tensions in Ukraine.

About four days later, American defense officials raised the security alert level at military bases in Europe in response to vague threats from the Kremlin over Ukraine’s use of long-range weapons on Russian territory.

American officials said that no specific intelligence about possible Russian attacks on American bases had been collected. Any such attack by Russia, whether overt or covert, would be a significant escalation of its war in Ukraine.

Russia has stepped up acts of sabotage in Europe, hoping to disrupt the flow of matériel to Ukraine. So far, no American bases have been targeted in those attacks, but U.S. officials said raising the alert level would help ensure that service members were keeping watch.

Then there were the calls on Oct. 21 and Oct. 23, 2022, between Mr. Austin and Mr. Shoigu — the first requested by the Americans, the second by the Russians.

The Pentagon’s summary of the second call stated, “Secretary Austin rejected any pretext for Russian escalation and reaffirmed the value of continued communication amid Russia’s unlawful and unjustified war against Ukraine.”

A week later, The New York Times reported that senior Russian military leaders had recently discussed when and how Moscow might use a tactical nuclear weapon in Ukraine, according to multiple senior American officials.

The new intelligence surfaced when Moscow was promoting the baseless notion that Ukraine was planning to use a so-called dirty bomb — a conventional explosive laced with radioactive material.

President Vladimir V. Putin of Russia was not a part of the conversations with his generals, which were held as Russia was intensifying nuclear rhetoric and suffering battlefield setbacks.

But the fact that senior Russian military leaders were even having the discussions alarmed the Biden administration because it showed how frustrated they were about their failures in Ukraine and suggested that Mr. Putin’s veiled threats to use nuclear weapons might not just be words.

While the risk of further escalation remained high, Biden administration officials and U.S. allies also said at the time that the phone calls between Western and Russian counterparts in late October helped ease some of the nuclear tensions.

“These calls are about avoiding worst-case outcomes in a relationship that could potentially go over the edge,” said Samuel Charap, a Russia analyst at the RAND Corporation.

Anton Troianovski contributed reporting from Berlin, and Marc Santora from Kyiv.

The swift Ukrainian incursion into Russia’s Kursk region that began last week has been the largest cross-border raid by Kyiv’s forces in the nearly 2 ½-year war, and has exposed Russia’s vulnerabilities and dealt a painful blow to the Kremlin.