The woman in the video, her face blurred, gave a blunt assessment of Russian military policy: Soldiers mobilized over a year ago to fight in Ukraine deserved to come home. Why weren’t they?

“Our mobilized became the best army in the world, but that doesn’t mean that this army should stay there to the last man,” she said. “If he did something heroic, spilled blood for his country sincerely, then maybe it was time to return to his family, make way for someone else, but that’s not happening.”

The speaker was part of a new, grass-roots movement that has been gathering steam in Russia over the past several weeks. Women in various cities are seeking to stage public protests, challenging the official argument that mobilized troops are needed in combat indefinitely to secure their Russian homeland.

Hand-lettered posters behind the speaker in the video echoed that sentiment with slogans like “Do only the mobilized have a homeland?” A video of the speech, delivered at a rally in the Siberian city of Novosibirsk on Nov. 19, was released online.

The nascent movement is a rare example of public displeasure with the war, the kind that the Kremlin has sought to suppress through draconian laws meant to stifle antiwar demonstrations. The women and the government officials have been involved in a delicate dance, with the protesters trying not to trigger those laws while the authorities seek to avoid hauling the relatives of active duty soldiers off to jail.

The authorities have so far stepped lightly, using intimidation and cajoling rather than detention or arrests. Permits to hold rallies in several major cities were denied, for example, and women in chat forums have complained about harassment.

Some said law enforcement officers visited them at home to inquire about their online activity and to warn them of the legal consequences of attending unauthorized rallies.

One main outlet for the protest movement has been a channel on the Telegram messaging app called “Put Domoy” in Russian, or “The Way Home,” which has attracted more than 14,650 participants since it was founded in September.

The channel’s organizers published a manifesto pressing for mobilized soldiers to be sent home after a year in the combat zone. “Military servicemen and their families — unite and fight for your rights,” the manifesto said in part.

The authorities in Moscow and in Krasnoyarsk, in Siberia, rejected recent requests for a rally permit, with officials citing as the reason a restriction on public assemblies that was created to combat Covid-19. In Moscow, about 20 demonstrators unfurled posters with slogans like “No To Indefinite Mobilization” at a Communist Party rally on Nov. 7. The police led them away but did not detain them.

Maria Andreeva, who helped organize the Moscow protest, said that the government had largely responded by offering more money and benefits to families of soldiers. “They agree to pay us even more, but only if we keep quiet,” she said in an interview. “Many women need their husbands and sons, not payments.”

Participants in protests across the country are fed up, Ms. Andreeva said. While crowing that more than 410,000 men have signed contracts to join the military this year, the government has brushed aside demands from the families to demobilize those drafted in 2022.

The rally in Novosibirsk, held by a different organization, was the result of a compromise between organizers and the local authorities. Instead of a demonstration on the streets, local civilian and military officials gathered in a government auditorium. The press was largely banned, and participants had to prove that they had a relative serving in Ukraine.

Chelyabinsk, a major Russian city in the center of the country, held a similar meeting in its City Hall.

In Novosibirsk, the organizers said that countless women across Russia were “boiling” because all their quiet appeals and petitions fell on deaf ears. “The situation drove us, our relatives, to despair, and those mobilized to a critical degree of fatigue, both physical and moral,” the group said in a statement.

The groups protesting take pains to stress that they are not unpatriotic and that they strive to respect the law. They say they are simply asking that the Kremlin introduce troop rotations.

When the Russian government implemented what it called a “partial mobilization” in September 2022, calling up 300,000 men, it said those conscripted would have to stay in the military until Mr. Putin decided that they could be discharged.

Having already enacted one mobilization, ordering another one would be politically unpopular. In the meantime, tens of thousands of Russian soldiers have been killed and wounded, including many in ongoing assaults in Ukraine at places like Avdiivka.

The official response to the demand for rotation has been indirect at best. Protest organizers noted that Sergei Shoigu, the defense minister, made a statement last December saying that replacing the mobilized troops was one reason to raise the number of soldiers overall.

But this past September Andrei Kartapolov, the chairman of Parliament’s defense committee, said there would be no rotation for troops in Ukraine, noting that “They will return home after the special military operation is completed.” A petition with tens of thousands of signatures sent to the Kremlin evoked a similar response, Russian press reports said.

“Our men are already physically and mentally tired of being there,” said Ms. Andreeva. “That’s enough! We must act!”

A generation ago, an antiwar movement that coalesced around mothers opposed to the war in Chechnya was a significant factor in prompting the Kremlin to end the war there. The authorities have tried to ensure that no similar national movement emerges out of the current protests.

The subject of rotations is a delicate matter for the Kremlin, which is seeking to make sure that any protests remain a regional issue and do not become national news that Mr. Putin would be forced to address, said Tatiana Stanovaya, who recently wrote about the subject in her analytical newsletter, R.Politik.

“The Ministry of Defense is cautious, preferring to boost soldier numbers whenever possible and keep them at the front,” wrote Ms. Stanovaya. She said any decision on a new mobilization wave “would be especially undesirable in the run-up to the presidential election next year.”

At a recent seminar focused on the presidential election in March, held in a town called Senezh, near Moscow, regional officials received specific instructions to prevent the women’s protest movement from metastasizing into something larger, according to Russian press reports.

The authorities said a demonstration could provide an opening for foreign powers to sow chaos, according to the business daily Kommersant, which is sympathetic to the Kremlin. But in a nod to the protesters’ frustration, the officials were told that they needed to stay in touch with the women, to pay attention to their problems and to help solve them, the report said.

Another Russia publication, the independent online newspaper The Insider, quoted an unidentified regional official as saying the preferred strategy was to “persuade, promise, pay” to avoid any kind of displeasure to be expressed on the streets.

Some participants hoped that the protests would spark a wider questioning of the war.

One woman in the chat group described herself in text messages as a longtime participant in antigovernment rallies. Although she does not have any relatives fighting in Ukraine, she believes that the women’s anti-mobilization movement has real potential to grow.

Communicating anonymously to avoid criminal charges for questioning the official narrative of the war, she said she hoped to seed the online discussions with information that depicted an alternative to the rosy official picture of the war, to “sow doubts about the truthfulness of the words of officials and the president (well, he’s lying all the time).”

By raising doubts, she said, she hoped “that people begin to ask questions, to be interested in politics, to be interested in what is happening in the country.”