"In an excellent conversation with Rishi Sunak we agreed to write a new chapter in Ukrainian-British relations," Zelensky announced in a tweet.
"But the story is the same - full support in the face of Russian aggression," he said.
Zelensky also tweeted on Tuesday that he appreciated Sunak's "first call to Ukraine" after taking over as prime minister, and said he was "grateful for the support of the British people."
Ukraine 'can count on UK's continued solidarity and support': Sunak
Sunak tweeted that it was "a privilege to speak to the President of Ukraine," adding that both Zelensky and the Ukrainian people "can count on the UK's continued solidarity and support."
"We will always stand with Ukraine," Sunak declared.
Earlier on Tuesday, Ukraine's Zelensky congratulated Sunak on becoming the new prime minister of Britain.
"Congratulations to Rishi Sunak on taking office as Britain's Prime Minister," Zelensky said in a tweet in English.
"I wish you to successfully overcome all the challenges facing British society and the whole world today," he added.
He also said he was "ready to continue strengthening the Ukrainian-British strategic partnership together."
Poland, UK 'standing together against Russian invasion of Ukraine': Polish president
Top Polish officials on Tuesday congratulated Sunak after his appointment as prime minister by King Charles.
Poland's President Andrzej Duda said in a Twitter post that Poland and Britain "are steadfast allies and are standing together against the Russian invasion of Ukraine."
Rishi Sunak on Tuesday promised to "work day in, and day out to deliver" for the British people as the UK's new prime minister. EPA/TOLGA AKMEN
Britain's previous prime minister, Liz Truss, said in late September that the UK would never accept Russia's attempted annexation of four regions of Ukraine.
Britain's government last month pledged to "match or exceed" its 2022 military support to Ukraine next year.
It said at the time that the UK was the second-largest military donor to Ukraine, after the United States, committing £2.3 billion in 2022, according to the gov.uk website.
Wednesday is day 245 of Russia's war on Ukraine.
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Source: PAP