MOSCOW - Struggling on the battlefield in southern and eastern Ukraine, Russia felt war on its own territory on Sunday as more than a dozen explosions ripped through a Russian border region, and a series of blasts severely damaged the offices of Russia's puppet government in the Ukrainian city of Donetsk.

The strikes in the Belgorod region next to Ukraine and the destruction of the municipal administration building in Donetsk, a city firmly controlled by Russia and its proxies since 2014, sent a powerful signal that the mayhem unleashed by Russian President Vladimir Putin's invasion is spreading far beyond the front lines.

The blasts, which Russia attributed to Ukrainian shelling, came a day after another sign of disarray in Russia's once-vaunted military machine: Two men opened fire on fellow Russian soldiers at a training camp in the Belgorod region, killing 11 and wounding 15 before being killed themselves.

The Russian Defence Ministry, in a statement cited by the state media outlets RIA Novosti and Tass, described the shootings as a terrorist attack. It said the two gunmen were from a former Soviet nation and had fired on the soldiers during target practice at a firing range.

The episodes, along with an Oct 8 attack on Russia's only bridge to Crimea, a region occupied by Moscow since 2014, added to a growing impression that what Mr Putin declared a "special military operation" in February has spiralled in dangerous new directions.

Belarus - Ukraine's neighbour to the north and a close ally of Russia from whose territory it launched an abortive attack on the Ukrainian capital in February - announced on Sunday that trains carrying Russian troops had arrived in preparation for the formation of a new joint Russia-Belarus force.

The Belarusian Defence Ministry said on Telegram that the "aviation component" of the new force, whose exact purpose has not been spelled out, had also started arriving from Russia.

Mr Alexander Lukashenko, Belarus' president, has repeatedly said that he does not want his military to join Russia's fight inside Ukraine, but analysts note that he emphatically denied that Russia would attack Ukraine from his territory just days before Russia did just that.

A renewed Russian offensive in northern Ukraine from Belarus would further expand a conflict that Russia initially expected to last just a few days but that has now raged for nearly eight months. The fighting has shred the reputation of Russia's military and of Putin, even among some of his supporters at home and abroad.

RIA Novosti reported that 16 explosions had hit Russia's Belgorod region, an important staging ground for its invasion. This was a sharp increase in what had previously been mostly isolated attacks, apparently by Ukraine, on Russian territory close to the border.

Ukrainian officials did not comment, in keeping with an official policy of near-total silence about explosions inside Russia's internationally recognised border.

When a suspected Ukrainian attack destroyed part of Russia's bridge to Crimea this month, Putin ordered an immense retaliatory strike on Kyiv and other Ukrainian cities. Britain's military intelligence agency reported on Sunday that Russia had fired 80 cruise missiles in those strikes but added that its capacity for future retaliation with missiles was severely constrained by production problems.

"Russia's defence industry is probably incapable of producing advanced munitions at the rate they are being expended," the report said. Russia's depletion of its long-range missile stock, the agency added, "is likely to constrain their ability to strike the volume of targets they desire in future."

Russian forces, driven from much of Ukraine's northeastern Kharkiv region last month by a lightning counteroffensive, have since slowed the advance of Ukrainian troops in the east. Russia has also recaptured some small villages and gained ground around the Ukrainian-held town of Bakhmut as it tries to reverse any narrative that it is losing.

Ukraine, which rarely reports setbacks and focuses instead on Russian defeats, said on Sunday that its forces had repelled a series of Russian attacks on settlements near Kramatorsk, a key Ukrainian-held city in the Donetsk region, and on Berestove, Soledar and Bakhmut, also in Donetsk.

Ukraine has also reported slow but steady gains around Kherson, the first major city captured by Russia at the start of the war.

Russian-appointed officials in occupied Kherson on Friday advised civilians to evacuate, a move that Ukrainian authorities trumpeted as a sign of panic in face of their army's advance toward the symbolically important city on the Dnieper River.

Sunday's violence in Belgorod and Donetsk city did not change the balance on the battlefield but did deliver a symbolic blow to Russian efforts to reset the narrative and to the Kremlin's desire to distance the Russian people from the war.

In Belgorod, colleges and businesses have conducted evacuation drills, local officials have evacuated towns and villages that have come under shelling and thousands of people from Ukraine have crossed the border to flee fighting, especially amid the recent Ukrainian counteroffensive. Sunday's explosions followed four successive days of sporadic strikes on the region, including what Russia says were Ukrainian attacks on an apartment building and a power station.

Donetsk city, the epicentre of Russian efforts to grab Ukraine's eastern Donbas region since 2014, has been hit before by Ukrainian artillery and sporadic street fighting, but Sunday's destruction of the main administrative building was the first time that a seat of Russian power in the city centre had been hit so hard.

Russian state-run news agency Tass reported that one man was killed and two others wounded when Ukrainian shelling struck the Donetsk city administration building.

The city is under the control of the so-called Donetsk People's Republic, a Russian proxy entity that Mr Putin declared part of Russia on Oct 5, along with three other regions. Last week an overwhelming majority of countries in the United Nations declared the land grab illegal; only four nations - North Korea, Belarus, Syria and Nicaragua - voted to support Russia.

Russia has claimed for years that Ukraine is committing "genocide" against ethnic Russians in the Donetsk region, an accusation unsupported by any evidence but used by Moscow as part of its pretext for invading Ukraine. It nonetheless seemed shocked by Sunday's strike in the centre of Donetsk city, previously a mostly safe area that senior Kremlin officials have visited in recent weeks.

Images and videos posted on social media appeared to show debris scattered throughout the building, smoke pouring from broken windows and cars on fire in the parking lot. NYTIMES