Ms Truss held the call with Mr Zelensky within hours of becoming Prime Minister.
It comes after US President Joe Biden congratulated Ms Truss on becoming Prime Minister and vowed to deepen the “special relationship” between the US and the UK.
In a statement, the Ukrainian president said he had thanked the British people for their support.
Mr Zelensky tweeted: “I became the 1st foreign leader to have a conversation with the newly elected (British) PM @trussliz. Invited her to (Ukraine). Thanked (British) people for the major defense & economic aid for (Ukraine). It’s important that (Britain) is ready to further strengthen it. Attention was paid to security guarantees.
“We discussed the participation of (Britain) in the recovery of (Ukraine). Coordinated further pressure on the RF (Russian Federation). The goal is to stop the aggression & bring the perpetrators to justice. It’s important to designate the RF a terrorist state. We’ll continue active interaction in all formats..”
A Downing Street spokeswoman said that Ms Truss had told the Ukrainian president that his country could count on the UK’s assistance “for the long term”.
“In her first call with a counterpart since becoming Prime Minister, she reiterated to the Ukrainian leader that he had her full backing, and Ukraine could depend on the UK’s assistance for the long term,” she said.
“President Zelensky thanked the Prime Minister for the UK’s staunch support and congratulated her on her appointment.
“The leaders discussed the need to strengthen global security and the measures necessary to cut off the funds fuelling Putin’s war machine.
“The leaders deplored Putin’s attempts to weaponise energy, and the Prime Minister said it was vital Russia’s blackmail did not deter the west from ensuring Putin fails. She also underscored the importance of ensuring the UK and our allies continue to build energy independence.”
The spokeswoman added that the Prime Minister was “delighted” to accept an invitation to visit Ukraine.
“She praised the Ukrainians’ fight for sovereignty and self-determination and said it was essential Ukraine succeeds and Russia fails,” she said.
“The Prime Minister said she looked forward to working with the president in the coming weeks and months and was delighted to accept an invitation to visit President Zelensky in Ukraine soon.”
Earlier, the US president was the first world leader to congratulate Ms Truss on her new position.
Just as Ms Truss finished her speech and formally entered Downing Street, the US president tweeted: “Congratulations to Prime Minister Liz Truss.
“I look forward to deepening the special relationship between our countries and working in close cooperation on global challenges, including continued support for Ukraine as it defends itself against Russian aggression.”
Mr Biden later spoke to the Prime Minister in a phone call.
A Downing Street spokeswoman said the pair reflected on the “enduring strength” of the special relationship and discussed the Belfast Agreement.
“The Prime Minister looked forward to working closely with President Biden as leaders of free democracies to tackle shared challenges, particularly the extreme economic problems unleashed by Putin’s war,” she said.
“The Prime Minister and President Biden reflected on the enduring strength of the special relationship. They agreed that the partnership between our countries, fortified by our shared values, has been crucial for defending and advancing freedom and democracy in the world.
“They agreed to build on those links, including by furthering our deep defence alliance through Nato and Aukus.
“The leaders reinforced their commitment to strengthening global liberty, tackling the risks posed by autocracies and ensuring Putin fails in Ukraine.
“The Prime Minister and President discussed a range of domestic issues and agreed on the importance of protecting the Belfast (Good Friday) Agreement.”