Aslin’s family has urged Britain and Ukraine to “do everything to get them back to us safely and quickly”, insisting the two men “are not and never were mercenaries”.
Truss said: “I strongly condemn the conviction of Aiden Aslin and Shaun Pinner by Russian proxies in eastern Ukraine.
“They are prisoners of war. This is a sham judgment without any legitimacy.
“My thoughts are with the families. We will continue to do everything we can to support them.”
There were concerns that making their case a bilateral matter between the UK and Russia would aid Moscow in its narrative that the men are “mercenaries” and therefore not entitled to protection under international law.
Britain argues that Aslin, from Newark in Nottinghamshire, and Pinner, from Bedfordshire, are members of the Ukrainian army and should therefore be treated as prisoners of war.
In a statement to the Newark Advertiser, Aslin’s family said: “We love Aiden with all our hearts. He and Shaun, as members of the Ukrainian Armed Forces, should be treated with respect, just like any other POW.
“They are not mercenaries and never were. We hope this verdict is overturned and we call on the governments of the UK and Ukraine to do everything in their power to get them back to us safely and quickly.
“We can only imagine what they are going through right now.”
A third man, the Moroccan national Saaudun Brahim, was convicted alongside Aslin and Pinner.
The men were accused of being “mercenaries” after fighting with Ukrainian troops.
The court where they were sentenced, which is not internationally recognized, is in the pro-Russian so-called Donetsk People’s Republic.
Interfax, a Russian news agency, claimed the men could appeal their convictions.
Aslin and Pinner were both members of regular Ukrainian military units that fought in Mariupol, the southern port city that has seen some of the heaviest fighting since Vladimir Putin’s invasion of Ukraine.
Former Tory minister Robert Jenrick, who represents the constituency where Aslin lived, called for the Russian ambassador to the UK to be summoned to the Foreign Office.
It comes after a friend of Aslin’s said the death sentences will “strengthen” those who still resist Russia’s advances.