Rishi Sunak will urge Narendra Modi to use his influence to help bring an end to the war in Ukraine, as he embarks on his first visit to India as the UK's premier.
The British prime minister will be meeting his Indian counterpart for one-to-one talks at the G20 summit, which he hopes will also smooth the way for a post-Brexit trade deal in the coming months.
But Downing Street has made clear there will be no changes to UK immigration policy as part of the deal - although short-term business visas will be up for discussion.
The Russian invasion - which India has refused to condemn - threatens to overshadow the summit of the world's wealthiest countries, which is being hosted in New Delhi for the first time.
As Mr Sunak set off for the trip, the prime minister's spokesman said: "We will use every opportunity to show our support for Ukraine and further foster global support as well.
"India has a vital role to play as the world's largest democracy in calling out Russia's assault on human rights and indeed democracy itself.
"We will use meetings with Modi or elsewhere to encourage them to use that influence to bring an end to Putin's brutal invasion."
Hopes of securing a trade deal between the UK and India during this trip - which would be the biggest agreement post-Brexit - have faded, but there are hopes of a later breakthrough.
Former prime minister Boris Johnson had promised a deal would be done by Diwali of 2022, but the autumn festival came and went, and significant issues in the negotiations remained.
However, government insiders are cautiously optimistic that the talks, now in their 12th round, are nearing the end, and a deal could be done later this year, with political will on both sides.
Mr Sunak is understood to be planning a second trip to India towards the end of the year. His spokesman said they did not have a firm deadline but it was expected the free trade agreement will be discussed with Mr Modi at this summit.
"The prime minister is committed to concluding an FTA [Free Trade Agreement] with India, which delivers for the British people, and this focus on delivering will run through all his engagement at the G20," the spokesman said.
Among those sticking points is understood to be the issue of visas, with India said to be seeking assurances on student and business visas.
The spokesman stressed there were "no plans to change our immigration policy, including on student visas", adding: "The PM has been clear that immigration levels are too high."
But he described India as "an indispensable partner for the UK".
Mr Sunak's aides described his first visit to India in office as an "historic moment" for the UK's first prime minister of Indian descent.
His rise to the leadership last year was viewed from the country with huge interest, with Indian broadcaster NDTV hailing the moment as: "Indian son rises over the empire" and "history comes full circle in Britain".
Mr Modi, who met Mr Sunak at last year's G20 summit in Bali, used his first message to the UK prime minister to say his victory would build a "living bridge to UK Indians".
The British leader will be accompanied on the trip by his wife Akshata Murty, who grew up in India and is the daughter of Narayana Murty, the founder of Infosys - one of the biggest companies in the country.
Outside the G20 official programme, they will visit a Hindu temple and watch a traditional Indian performance with Mr Modi and his wife.
Russia looms over summit
Russian President Vladimir Putin, who remains a G20 leader, is not attending the summit for the second year running, but will send foreign minister Sergey Lavrov.
Downing Street said there were no plans for any engagement, but said Mr Sunak would "use any opportunity in sessions to remind Lavrov to his face about the damage Russia is doing to Ukraine and globally".
Agreeing a joint communique or declaration - a feature of every G20 summit since it was set up in 2008 - will be a key challenge for the Indian hosts.
Last year's summit in Bali produced an unusual one, noting that "most members" condemned Russia's invasion of Ukraine, and demanded its unconditional withdrawal.
David Lammy MP, Labour's shadow foreign secretary, said: "Rishi Sunak arrives at the G20 as a minnow on the global stage.
"This G20 cannot just be used as an opportunity for personal networking and Instagram content.
"Britain needs a prime minister who will use the G20 to rebuild our credibility with key allies in the US and the EU, while forging new partnerships on trade, climate and critical minerals with rising powers."