Major battlefield gains by pro-Russia rebels in eastern Ukraine may be absorbing the full attention of Kiev and Moscow, in large part thanks to an all-but-openly-acknowledged boost in Russian assistance to the rebels' cause.

But leaders in both capitals may soon need to take account of growing doubt among their respective publics. Russians are beginning to see how embroiled they are in a war they don't want. And Ukrainians are growing weary of the conflict in the east when other daunting problems loom.

Ukraine argues that its recent military reverses have been caused by the direct intervention of Russian troops. President Petro Poroshenko canceled a planned visit to Turkey on Thursday to deal with the crisis. Moscow and rebel leaders deny that Russian soldiers or hardware are directly involved in the conflict.

But the prime minister of the self-proclaimed Donetsk Peoples Republic, Alexander Zakharchenko, said Thursday that up to 4,000 Russian "volunteers" have been fighting alongside the insurgents. "We have never concealed that many Russians are fighting in our ranks without aid of which we would be in a very difficult situation," the official ITAR-Tass agency quoted him as saying.

An unwanted war

Mr. Zakharchenko added that Russian volunteers "unfortunately sustained some casualties" – a comment that will fuel a dawning controversy in Russia.

Opinion polls continue to show robust public support among Russians for the east Ukrainian rebels, with 55 percent saying in August that they support the movement of Russian volunteer fighters into Ukraine to back up the insurgents, according to Alexei Grazhdankin, deputy director of the independent Levada Center in Moscow.

But the number of Russians who would support sending Russian troops to fight in Ukraine has fallen from 28 percent in April, to 16 percent this month.

News that Russian troops may already be fighting – and dying – in Ukraine is starting to appear in the Russian media. Several independent Russian news outlets have reported secret military funerals in recent days. A regional chapter of Russia's oldest anti-war group, the Committee of Soldier's Mothers, has drawn up a list of 400 Russian servicemen who have died or been wounded under suspicious circumstances.

And journalists who've tried to follow up on the reports have been attacked and threatened. Two reporters for the liberal TV station Dozhd attempted to talk with family members at a funeral of several paratroopers in Pskov, but were surrounded by young toughs and told to "head to the train station and take the first train back to Moscow."

The steady trickle of dead Russians returning from Ukraine could eventually have a powerful negative impact on public opinion, and that's why it's being kept secret, says Valentina Melnikova, head of the Union of Committees of Soldiers' Mothers in Moscow.

"These secret burials remind me of how it was around [the Soviet war in Afghanistan] in the 1980s. Nothing has changed since those days. There is no official data, nobody writes about it, and we can't find out how many of them have died," she says. "In six months or so, families will understand that they've been betrayed, and then maybe we'll find out...."

Kremlin spokesman Dmitry Peskov indirectly acknowledged the issue's sensitivity by agreeing with a journalist that the reports of dead Russian servicemen in Ukraine should be thoroughly investigated.

'Why should we lose our sons for Donbass?'

The war is also taking a public toll in Ukraine, where the military reverses of recent days have reportedly triggered public protests against the corruption and official incompetence which many hold responsible for the army's failure to defeat the rebels.

The commander of the pro-Kiev Donbass militia, Semyon Semenchenko, organized a protest in downtown Kiev Wednesday to demand authorities immediately dispatch reinforcements to save the group, which is reportedly surrounded by rebel fighters in the town of Ilovaysk, near Donestk. On his Facebook page, Mr. Semenchenko accused Ukrainian generals of deceiving him and abandoning his men to their fate. He added that unless help arrives soon, Ilovaysk will become "a mass grave."

Vladimir Paniotto, director of the independent Kiev International Institute of Sociology, Ukraine's leading pollster, says that support for the war among Ukrainians is showing signs of softening as hope for a quick military victory has evaporated, and the costs of war have escalated.

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"People are dying, while corruption in authorities' circles remains rampant," says Vadim Karasev, director of the independent Institute of Global Strategies in Kiev. "There is a third [conscription drive] underway, and it's not going well. Mothers are against it, and now they're taking to the streets in many communities around Ukraine, even blocking roads. 'Why should we lose our sons for Donbass? Let it go,' you hear people saying more and more often."

"There's still some enthusiasm for the fight, particularly in right-wing circles," Mr. Karasev adds, "but the overall mood overtaking society is one of exhaustion."