Several world leaders, including US President Joe Biden and Ukraine's President Volodymyr Zelenskyy, have lauded Rishi Sunak becoming the UK's new Prime Minister as a "ground-breaking milestone" and hoped for better bilateral relations amidst a turbulent world.

Sunak, 42, on Monday, won the race to lead the Conservative Party and became Britain's first prime minister of Indian-origin on Tuesday.

Sunak will be the third UK prime minister this year and will replace Liz Truss, who served as Britain's shortest-serving prime minister for just 45 days.

"We've got the news that Rishi Sunak is now the prime minister," Biden said in remarks made during a Diwali celebration at the White House on Monday.

"It's pretty astounding, a groundbreaking milestone and it matters," the US President said.

Biden is yet to formally congratulate Sunak until he has met King Charles and been asked to form a government, as protocol dictates.

The Kremlin on Tuesday said that Russia sees no reason to expect relations with the UK to improve under Sunak.

Russia does not see any "preconditions, grounds, or hope" for building more constructive relations with Great Britain in the foreseeable future, Kremlin Spokesman Dmitry Peskov said, commenting on the appointment of Sunak as the UK's new prime minister.

"No, at present, we do not see any preconditions, grounds or hopes for some positive shifts in the foreseeable future," the Russian presidential spokesman was quoted as saying by the official TASS news agency.

Peskov said this while commenting on the prospects of warmer relations between the two countries with the appointment of the UK's new prime minister.

Russia-UK relations have soured even further since Russia's invasion of Ukraine in February. The UK responded with several rounds of sanctions, and it is one of the main backers of President Volodymyr Zelensky. The UK has also provided substantial military support to Ukraine, the report added.

Ukraine's President Zelenskyy tweeted his congratulations to Sunak. "I wish you to successfully overcome all the challenges facing British society and the whole world today. I'm ready to continue strengthening the Ukraine-UK strategic partnership together!" he said.

China's leadership has said that it wants to "advance ties with the UK" under Sunak, Foreign Ministry spokesman Wang Wenbin was quoted as saying by the BBC.

"We hope that we can work with the UK side on the basis of mutual respect and win-win co-operation and advance China-UK relations along the right track," he said.

Sunak has favoured closer ties with China than his predecessor and was criticised by Truss for pursuing a trading relationship when chancellor, the report added.

Australia's treasurer, Jim Chalmers, called Sunak a great friend of Australia and lauded the significance of Britain having its first prime minister of Asian descent, The Canberra Times newspaper reported.

"I don't think it's insignificant that a country like the United Kingdom has its first prime minister of colour," he said on Tuesday.

European leaders couched their well-wishes with statements on the need for a stable and predictable neighbour.

The European Council president, Charles Michel, tweeted his congratulations on Monday night, emphasising that Brussels and London faced shared challenges.

"Working together is the only way to face common challenges... and bringing stability is key to overcoming them," he wrote.

The president of the European Parliament, Roberta Metsola, said the EU legislature was committed to having "a strong and constructive relationship with the UK".

"At a time of enormous challenges, Europe needs political and economic stability. Our core interests remain the same," she said.

New Zealand's Deputy Prime Minister Grant Robertson says the new British leader is a "good friend" of his country, the NZ Herald reported.

He hoped the Tory leader would help seal a free trade agreement with his country.

"Clearly, the UK is facing some very significant economic issues at the moment, he's said that himself. Inflation up over 10 per cent, the energy crisis, the war in Ukraine, so it's going to be a very tough time for him," he said.

"So, we wish Rishi Sunak well. I personally look forward to working with whoever he names as chancellor of the exchequer."

Irish Prime Minister Miche l Martin said he looked forward to working with Sunak, "on the important issues we face on these islands and globally".