Mr Biden began the calls by congratulating Ms Truss on her appointment.
The prime minister said she looks forward to working closely with Mr Biden to tackle shared challenges, particularly the war in Ukraine.
The leaders also discussed the importance of protecting the Belfast (Good Friday) Agreement and expressed their wish to meet each other soon.
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Ms Truss is expected to travel to the US later this month for the UN General Assembly, where she will be hoping for her first face-to-face meeting with the president.
During Ms Truss's call with Mr Zelenskyy, she pledged to visit Ukraine soon.
Ms Truss held the call with Mr Zelenskyy within hours of becoming prime minister.
In a statement, the Ukrainian president said he had thanked the British people for their support.
“I became the first foreign leader to have a conversation with the newly elected [British] PM @trussliz,” he tweeted.
“Invited her to [Ukraine]. Thanked [British] people for the major defence and 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]. Co-ordinated further pressure on the RF [Russian Federation]. The goal is to stop the aggression and 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 Zelenskyy 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 Mr Putin’s war machine.
“The leaders deplored Mr 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.”
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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 Zelenskyy in Ukraine soon.”