“We are determined to provide more weapons, impose more sanctions and back Ukraine in pushing Russia out of their territory,” the Foreign Secretary told parliament.
Ms Truss said she would be travelling to Turkey on Wednesday to discuss options to help get grain out of Odesa, saying that there was only a matter of weeks to find a solution.
Britain, the United States and the European Union have coordinated in imposing massive sanctions on Moscow since it invaded Ukraine on February 24.
“We will continue to impose sanctions, we will continue to stop importing goods from Russia until we see Russia fully withdraw from Ukraine,” Ms Truss said.
Britain has targeted Russian businessmen, politicians, religious leaders and businesses as part of its wide-ranging sanctions on Moscow.
Ukrainian officials said Russia intensified its onslaught on two key cities in the east on Monday - and described a lull in fighting overnight as the “calm before the storm”.
Ukrainian President Volodymyr Zelensky had predicted Russia would step up attacks ahead of the EU summit on Thursday and Friday.
He was defiant in a late Monday address to the nation, while also referring to “difficult” fighting in Luhansk for Severodonetsk and its sister city, Lysychansk.
“We are defending Lysychansk, Severodonetsk, this whole area, the most difficult one. We have the most difficult fighting there,” he said. “But we have our strong guys and girls there.”
The governor of the Luhansk region, scene of the heaviest Russian onslaughts in recent weeks, said Russian forces had launched a massive attack and gained some territory on Monday though it was relatively quiet overnight.
"It's a calm before the storm," the governor, Serhiy Gaidai, said.
Mr Gaidai said Russian forces controlled most of Severodonetsk, apart from the Azot chemical plant, where more than 500 civilians, including 38 children, have been sheltering for weeks. The road connecting Severodonetsk and Lysychansk to the city of Bakhmut was under constant shell fire, he said.
Rodion Miroshnik, ambassador to Russia of the self-styled Luhansk People’s Republic, said its forces were “moving from the south towards Lysychansk” with firefights erupting in a number of towns.
“The hours to come should bring considerable changes to the balance of forces in the area,” he said on Telegram.