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They estimate more than 15,000 Russian military personnel have been killed, though “not necessarily significantly more” than this figure given several weeks ago as Mr Putin has scaled back his military campaign to focus on the Donbas region in the east of the country.
“The number of wounded in action is probably north of 40,000 Russian wounded in action,” said one official.
This high figure is thought to be partly due to how Russian generals have thrown soldiers into dangerous advances, to the strength of Ukrainian resistance and weapons supplied by western nations.
But western officials also believe Mr Putin’s forces have been deployed with a lack of medical support, partly as he mistakenly expected them to be welcomed as liberators.
“Some units deployed in this operation have deployed without anything remotely like adequate medical support so when they do take casualties those casualties are not able to be triaged and treated appropriately,” said one official.
Ukrainian casualties are believed to be between 60 and 100 soldiers killed a day.
Mr Putin’s troops are advancing in parts of eastern Ukraine at as little as 500 metres on average a day as they are being hit by fierce resistance, according to the western officials.
They stressed Russian generals would have planned to gain territory at tens of miles a day.
Mr Putin’s military operation is focusing on seizing territory in the Donbas region and his forces are believed to have now captured more than half the city of Severodonetsk.
The Russian offensive is being led by heavy artillery bombardments, reducing parts of towns, cities and villages to ruins in south east Ukraine, before troops try to move forward.
“It’s making slow but steady gains, largely achieved through its doctrine of concentrating indirect fire, immense firepower in order to then grind through the movement,” said one official. “It’s interesting to look on the axis from Popasna where forces have been advancing against that pocket.
“Over the last month, they have averaged between 500 metres and a kilometre (0.62 miles) a day in terms of their advance. Doctrinally, they would be looking for tens of kilometres for an advance of this nature.
“It gives an indication of the challenge of the nature of the terrain, the challenges that Russia is having in terms of their operations but also the ferocity of Ukrainian resistance.
“So, the fight is ongoing, Russia is making incremental but pretty steady gains all be it at a relatively slow pace.”
US President Joe Biden has announced that Washington is sending high-tech, medium-range multiple launch rocket systems to Ukraine where Mr Putin’s superior artillery firepower has so far allowed it to make advances in the Donbas.
“It gives a range of about 80 km (50 miles) and it’s a weapon system which is highly mobile and is particularly effective in terms of being able to engage targets and move or engage multiple targets in very quick succession,” said the western official.
“In that it outperforms the other systems that Russia is fielding in the battlespace.”
So Ukrainian forces will be able to more effectively target Russian artillery positions and also supply lines.
The rocket systems could have a “significant impact in terms of range and lethality” on the fighting in the Donbas.
They are part of a new $700 million (£553 million) tranche of security assistance for Ukraine from America that will include helicopters, Javelin anti-tank weapon systems, tactical vehicles, spare parts and more, according to two senior US administration officials.
The tight focus of the Kremlin’s military campaign, while making advances, means that it is also vulnerable on its operational flanks, with Ukrainian forces launching limited counter-attacks and seizing some territory in the Kherson province which is “relatively lightly held by Russia”.
Western officials believe that such a scenario could develop over coming months with Mr Putin’s troops being targeted in areas where they do not have high numbers deployed.
But his generals appear to have learned lessons from some of the blunders which forced them to abandon his lightning invasion plan, which included seizing Kyiv within days, and to retreat from around the capital and from swathes of northern Ukraine.
“We are seeing a more credible and slightly more well thought-through military concept of operations and we are seeing the impact both of the concentration of artillery but also some increasing effectiveness of the use of tactical air in support of those operations,” said the official.
The Russian air force, though, is still believed to be largely operating over its own positions, rather than Ukrainian ones given the risk from air defence systems, limiting its impact “in depth”.
If Severodonetsk falls to Mr Putin’s forces they will face more challenging objectives including seizing the key railway city of Kramatorsk to gain control of the whole of the Donbas.
The Russian president is still believed to be set on “maximalist” aims of capturing large swathes of Ukraine beyond the Donbas even though they are “a very long way from the Russian ability to deliver on them at the moment”.
Russian ground forces which were deployed for the operation are believed to have now been “written down” to just over 50 per cent combat effectiveness given the huge loss of troops and equipment, and they have now had to resort to rolling out 50-year-old T-62 tanks.
In contrast, Ukraine’s army, even though it is also suffering heavy losses, is being re-supplied with western weapons.
But the war is expected to last at least until the end of this year, if not considerably longer.
Defensive preparations are being made by both armies, including reinforcing supply routes, ahead of a possible summer of battles and in recognition that advances are difficult to make on multiple, very wide fronts.
“It is likely that there will need to be certainly an operational pause and maybe a series of them depending on the duration of the campaign,” the official added.
“We have moved to a grinding more attritional struggle.”
Russian forces are also said to be suffering from “outbreaks” of low morale among soldiers at unit level and also among more senior officers, according to the western official.