Ukrainian forces have either destroyed or damaged all three of the bridges over the Seym River in western Russia, according to Russian sources, as Kyiv's incursion into western Russia entered its third week Tuesday.

Kyiv's incursion into Russia's Kursk region is changing the trajectory of the war and boosting morale among Ukraine's war-weary population, though the ultimate outcome of the incursion — the first attack on Russia since the Second World War — remains impossible to predict.

Even as Ukraine hails its success on Russian territory, the Russian push in eastern Ukraine is poised to claim another key centre: the city of Pokrovsk.

Ukraine's attacks on the Seym River bridges could potentially trap Russian forces between the river, the Ukrainian advance and the Ukrainian border. Already they appear to be slowing down Russia's response to the Kursk incursion, which Ukraine launched on Aug. 6.

Former U.S. ambassador's take on early days of Ukraine's Kursk offensive: 

Former U.S. Ambassador to Russia John Sullivan analyzes Ukraine’s incursion into Russian territory

Over the weekend, Ukraine's air force commander posted two videos of bridges over the Seym being hit, and satellite photos by Planet Labs PBC analyzed Tuesday by The Associated Press confirmed that a bridge in the town of Glushkovo had been destroyed.

A Russian military investigator confirmed Monday that Ukraine had "totally destroyed" one bridge and damaged two others in the area. The full extent of the damage remained unclear.

"As a result of targeted shelling with the use of rocket and artillery weapons against residential buildings and civilian infrastructure in the Karyzh village ... a third bridge over the Seym River was damaged," the unnamed representative for Russia's Investigative Committee said in a video published on the Telegram channel of Russian state TV anchor Vladimir Solovyov.

Russian military bloggers Vladimir Romanov and Yuri Podolyaka and several high-profile pro-war Telegram channels in Russia also claimed that the third bridge had been targeted and damaged. Podolyaka's post was shared by Roman Alekhin, an advisor to Kursk's acting regional governor.

Since the incursion into the Kursk region began, the Ukrainian army has captured 1,263 square kilometres and 93 settlements, Ukraine's top military commander said Tuesday — up from 1,000 square kilometres last week. Gen. Oleksandr Syrskyi made the remarks while meeting with local officials.

Ukraine reaching 'set goals': Zelenskyy

Following a meeting with Syrskyi later Tuesday, Ukrainian President Volodymyr Zelenskyy said that the Ukrainian army was achieving "set goals" in Kursk.

Zelenskyy said in recent days that the operation is aimed at creating a buffer zone that can prevent future attacks on his nation from across the border, and that Ukraine is capturing a large number of Russian prisoners of war that it hopes to exchange for captured Ukrainians.

The Russian state news agency Tass reported that 17 people have died and 140 have been injured in Ukraine's incursion, citing an unnamed source in the Russian medical service. Of 75 people hospitalized, four are children. Russia's Ministry of Emergency Situations said Tuesday afternoon that more than 500 people had left dangerous areas in the Kursk region over the past 24 hours. In total, more than 122,000 people have been resettled since the Ukrainian attack began, it said.

In another example of Ukraine taking the war to Russian soil, a massive fire burned for the third consecutive day after an oil depot was hit by Ukrainian drones.

The fire at the depot in the town of Proletarsk burned across an area of a hectare, according to Russian state news agencies. There were 500 firefighters involved in the operation, and 41 of them already have been hospitalized with injuries, according to Tass, citing local officials.

Ukraine's Army General Staff claimed responsibility Sunday for attacking the oil depot, which was used to supply the needs of Russia's army.

Putin accuses Ukraine of 'trying to destabilize'

Russian President Vladimir Putin accused the Ukrainians of "trying to destabilize our country" and compared them to terrorists. "We will punish the criminals. There can be no doubt about that," Putin said Tuesday.

Ukraine's incursion has exposed Russian vulnerabilities according to analysts and Ukrainian officials.

Zelenskyy said Monday that he believes Ukraine's actions would help to dispel Western fears of offering more robust military aid to Kyiv. Some allies have been handing over weapons slowly and imposing limits on how they can be used, fearing that crossing a Russian "red-line" could lead to escalation — even nuclear escalation.

Much remains unknown about Ukrainian operations in Russia but satellite images provide some clues.

Pontoon bridges — temporary bridges used by militaries when formal bridges are blown out — could be seen in the satellite images provide by Planet Labs PBC in two different positions along the Seym River in recent days. The pontoons likely were built by Russian troops trying to supply forces around the Ukrainian advance.

One pontoon bridge appeared along the serpentine path of the river between Glushkovo and the village of Zvannoye on Saturday, but not in images taken Monday. On Monday, smoke could be seen rising along the banks of the river nearby — typically the sign of a strike.

Meanwhile along the frontline in eastern Ukraine, Russia continued to bear down on the city of Pokrovsk, one of Ukraine's main defensive strongholds and a key logistics hub in the Donetsk region, forcing Kyiv's forces to pull back and Ukrainian civilians to flee their homes. Its capture would compromise Ukraine's defensive abilities and supply routes and would bring Russia closer to its stated aim of capturing the entire Donetsk region.

Russia's relentless six-month slog across the region following the capture of Avdiivka in February has cost both sides heavily in troops and armour.

Russia wants control of all parts of Donetsk and neighbouring Luhansk, which together make up the Donbas industrial region.