Dozens are feared dead after the school in Bilohorivka in the Luhansk region of eastern Ukraine was bombed and caught fire on Saturday.
Around 90 people were thought to have been sheltering at the school but just 30 have been rescued. Ukraine President Volodymyr Zelensky said around 60 people had been killed.
Ms Truss tweeted: “Horrified by Russia’s latest attack on a school in Luhansk, resulting in the deaths of innocent people sheltering from Russian bombardment.”
She said the deliberate targeting of civilians and infrastructure “amounts to war crimes” and “we will ensure Putin’s regime is held accountable”.
Her comments came as G7 leaders including Boris Johnson and Joe Biden prepare for talks with Ukraine’s president Volodymyr Zelensky.
A defence intelligence update said: “Difficulties in command and control, as well as faltering Russian performance on the front line, have drawn senior commanders onto the battlefield, likely to take personal leadership of operations.”
This has put them at risk of being targeted, with “disproportionately high losses of Russian officers in this conflict”.
“This has resulted in a force that is slow to respond to setbacks and unable to alter its approach on the battlefield,” the update said.
“These issues are likely to endure given the relative lack of operational command experience of the officers promoted in place of those killed.”
The UK has pledged an extra £1.3 billion in military support to Ukraine, in a dramatic escalation of assistance for Mr Zelensky’s forces as they fight the Russian invasion.
It is the highest rate of UK military spending on a conflict since the height of the campaigns in Iraq and Afghanistan.
The £1.3 billion, drawn from the UK’s reserves, includes £300 million of military kit promised by Mr Johnson earlier this week, such as anti-battery radar systems to target Russian artillery, GPS jamming equipment and night vision devices.
The Prime Minister will host a meeting of arms companies later this month to discuss increasing production in response to the demand created by the conflict in Ukraine.
Officials said the announcement would help support the British arms industry, which could benefit from the global shift away from reliance on equipment from sanctions-hit Russia.
The Prime Minister said: “Putin’s brutal attack is not only causing untold devastation in Ukraine, it is also threatening peace and security across Europe.
“The UK was the first country to recognise the scale of the threat and send arms to help the Ukrainians defend themselves.
“We will stand by that endeavour, working with our allies to ensure Ukraine can continue to push back the Russian invasion and survive as a free and democratic country.
“In the process, we are bolstering our own security and economy, turbocharging the development and production of cutting-edge defence equipment here in the UK.”