Russia's invasion of Ukraine is grinding towards the beginning of its third month and with Moscow's military advance and negotiations largely stalled there seems no immediate end to the fighting.

Here's what we can say definitively about the human cost from the conflict in which allegations of Russian atrocities have spurred fears of a massive civilian death toll.

The benchmark today in many global conflicts is the United Nations, which as of Tuesday this week estimated that in Ukraine there had been "4,450 civilian casualties in the country: 1,892 killed and 2,558 injured."

The UN however makes clear it "believes that the actual figures are considerably higher," citing delayed reported from the battlefield and efforts to verify existing reports.

In light of this, the UN announced last week it would change its methodology and release figures that reflect "a realistic estimate of the actual death toll," the head of its civilian casualty monitoring team said.

The UN tally doesn't include military deaths.

The defence ministries of both Ukraine and Russia regularly publish claims of the number of troops they have killed from the opposing side.

Kyiv says its troops have killed 19,600 Russian military since the invasion began in late February. Moscow said on March 25 its forces had killed at least 14,000 Ukrainian miliary personnel.

These figures, however, are both widely suspected to be inflated and have not been verified by AFP or independent conflict monitors.

Russia has, unusually, acknowledged its own military casualties but put the number of its dead much lower than Ukraine's claim at 1,351 in its last update on March 25.

A senior NATO military official estimated at the same time that between 7,000 and 15,000 Russian soldiers could have been killed in the fighting up to that point.

Kremlin spokesman Dmitry Peskov admitted last week to Sky News that Russian troops had suffered "significant losses" in Ukraine, calling it a "huge tragedy".

Bodies being exhumed from a mass-grave in Bucha
Bodies being exhumed from a mass-grave in Bucha AFP / Sergei SUPINSKY

Ukraine does not deny that its soldiers are dying on the battlefield but it has not published a total.

The withdrawal of Russian troops from towns around the Ukraine capital Kyiv has revealed mass civilian casualties and those figures look set to grow.

Bucha, where hundreds of corpses -- some with their hands tied behind their backs -- were discovered has become the most infamous location, but Ukrainian authorities are discovering similar scenes in other liberated areas.

Ukrainian police said Tuesday that so far, 720 bodies had been recovered in the Kyiv region.

North of Kyiv, authorities in Chernigiv -- the largest settlement to be recaptured from Russian forces said that some 700 people had been killed since the start of fighting.

In the eastern town of Severodonetsk, where fighting is still raging, officials said at least 400 civilians have been buried since the start of the invasion.

Clean-up and de-mining efforts are continuing in regions wrested from Russian control, and are expected to bring with them a higher count.

Perhaps the largest -- and most worrying -- question mark surrounds the southern city of Mariupol, which has been besieged by Russian forces for weeks. Ukraine troops are holding out in a major industrial plant.

Ukraine's President Volodymyr Zelensky said this week he believed Russia was responsible for the deaths of "tens of thousands" of people.

Donetsk region governor Pavlo Kyrylenko estimated on Tuesday that between 20,000 and 22,000 people had died in the city.

Kyiv officials said last month that as early as the beginning of March the confirmed deaths were already around 5,000 but by that point it could already have been as high as 10,000.

Ukraine's human rights ombudswoman on Thursday claimed Russia was utilising 13 mobile crematoria to "clean the streets from the bodies of dead civilians", efforts that if confirmed would make establishing an accurate toll in the city all the more difficult.