After more than four months of fighting, Russia has claimed a key victory in Ukraine: full control over one of the two provinces in its eastern industrial heartland.

But Moscow's seizure of the last major stronghold of Ukrainian resistance in Luhansk province came at a steep price. The critical question now is whether Russia can muster enough strength for a new offensive to complete its capture of the Donbas and make gains elsewhere in Ukraine.

Oleh Zhdanov, a military analyst in Ukraine, said: "Yes, the Russians have seized the Luhansk region, but at what price?"

He noted that some Russian units involved in the battle had lost up to half of their soldiers.

Even Russian President Vladimir Putin acknowledged on Monday that Russian troops involved in action in Luhansk need to "take some rest and beef up their combat capability".

That raises doubts about whether Moscow's forces and their separatist allies are ready to quickly thrust deeper into Donetsk, the other province that makes up the Donbas.

Observers estimated in recent weeks that Russia controlled about half of Donetsk, and battle lines have changed little since then.

What happens in the Donbas could determine the course of the war. If Russia succeeds there, it could free up its forces to grab even more land and dictate the terms of any peace agreement.

If Ukraine, on the other hand, manages to pin the Russians down for a protracted period, it could build up the resources for a counter-offensive.

Exhausting the Russians has long been part of the plan for the Ukrainians, who began the conflict outgunned - but hoped Western weapons could eventually tip the scales in their favour.

They are already effectively using heavy howitzers and advanced rocket systems sent by the US and other Western allies, and more is on the way. But Ukrainian forces have said they remain badly outmatched.

Ukraine's defence minister Hanna Malyar said recently that Russian forces were firing 10 times more ammunition than the Ukrainian military.

After a failed attempt at a lightning advance on the capital of Kyiv in the opening weeks of the war, Russian forces withdrew from many parts of northern and central Ukraine and turned their attention to the Donbas, a region of mines and factories where Moscow-backed separatists have been fighting Ukrainian forces since 2014.

Since then, Russia has adopted a slow-and-steady approach that allowed it to seize several remaining Ukrainian strongholds in Luhansk over the course of recent weeks.

While Ukrainian officials have acknowledged that their troops have withdrawn from the city of Lysychansk, the last bulwark of their resistance, the presidential office said on Tuesday the military was still defending small areas in Luhansk.

Mr Zhdanov predicted that the Russians would likely rely on their edge in firepower to "apply the same scorched earth tactics and blast the entire cities away" in Donetsk.

The same day that Russia claimed it had taken the last major city in Luhansk, new artillery attacks were reported in cities in Donetsk.

However, Russia's approach is not without drawbacks. Moscow has not given a casualty count since it said some 1,300 troops were killed in the first month of fighting, but Western officials have said that is just a fraction of the real losses.

Since then, Western observers have noted that the number of Russian troops involved in combat in Ukraine has dwindled, reflecting both heavy attrition and the Kremlin's failure to fill up the ranks.

The limited manpower has forced the Russian commanders to avoid ambitious attempts to encircle large areas in the Donbas, opting for smaller manoeuvres and relying on heavy artillery barrages to slowly force the Ukrainians to retreat.

The military has also relied heavily on separatists, who have conducted several rounds of mobilisation, and Western officials and analysts have said Moscow has increasingly engaged private military contractors.

It has also tried to encourage the Russian men who have done their tour of duty to sign up again, though it is is unclear how successful that has been.

While Mr Putin so far has refrained from declaring a broad mobilisation that might foment social discontent, recently proposed legislation suggested that Moscow was looking for other ways to replenish the ranks.

The bill would have allowed young conscripts, who are drafted into the army for a year and barred from fighting, to immediately switch their status and sign contracts to become full professional soldiers. The draft was shelved amid strong criticism.

Some Western officials and analysts have argued that attrition is so heavy that it could force Moscow to suspend its offensive at some point later in the summer, but the Pentagon has cautioned that even though Russia has been churning through troops and supplies at rapid rates it still has abundant resources.

If Russia wins in the Donbas, it could build on its seizure of the southern Kherson region and part of the neighbouring Zaporizhzhia to try to eventually cut Ukraine off from its Black Sea coast all the way to the Romanian border.

If that succeeds, it would deal a crushing blow to the Ukrainian economy and also create a corridor to Moldova's separatist region of Transnistria that hosts a Russian military base.

But that is far from assured. Mykola Sunhurovsky of the Razumkov Centre, a Kyiv-based think tank, predicted that growing supplies of heavy Western weapons, including HIMARS multiple rocket launchers, will help Ukraine turn the tide of the war.

"Overall, local military balance in Donbas favours Russia, but long term trends still favour Ukraine," wrote Michael Kofman, a US-based expert on the Russian military.

"However, that estimate is conditional on sustained Western military assistance, and is not necessarily predictive of outcomes. This is likely to be a protracted war."