Mr Sunak, who described his conversation with Mr Modi as “warm and productive”, told broadcasters in New Delhi on Saturday: “There is a desire on both of our parts to see a successful trade deal concluded.
“The opportunities are there for both countries, but there is a lot of hard work that is still to go and we need to work through that, as we will do.”
Downing Street said the premiers signed off on ministers and negotiating teams continuing to work “at pace” towards a free trade deal.
A trade pact with India, an agreement that could grant more favourable access for British companies to a market of 1.4 billion people, is seen as a major post-Brexit prize by the Conservative UK Government.
The Prime Minister, who is the first British leader of Indian descent, told reporters during his flight from London to New Delhi on Thursday that an agreement was “not a given” but his comments have gradually become more positive since arriving at the G20.
On Friday, he told Indian broadcaster Asian News International that “enormous progress” had been made before going further with his most recent remarks, suggesting the final obstacles could be worked through.
The deal is reportedly being held up by a variety of issues, including a disagreement over the number of visas for Indians to work in the UK and differences over the level of access British car manufacturers should be given to India’s market.
Mr Sunak, unlike his predecessor Boris Johnson, who wanted to seal a deal in time for October 2022 Diwali celebrations, said he would not set “arbitrary deadlines” for finalising an agreement.
With reports suggesting he could return to India in the autumn, the Indian government’s aim of ratifying fresh trade terms by the end of the year could be met.
Where differences can be seen between London and New Delhi has been in their stance on Russia’s invasion of Ukraine.
Mr Sunak has been outspoken in condemning Russian president Vladimir Putin’s 19-month assault on Kyiv while India has kept ties open with the Kremlin since Moscow’s forces crossed the Ukrainian border in February 2022.
The Tory leader would not confirm whether he pressed his counterpart to take a firmer stance on Russia.
He told broadcasters he thought a “very strong” joint message about Moscow’s attack had been made “under Prime Minister Modi and India’s presidency” of the G20, a group of the world’s largest economies that includes Russia and China.
A communique published on Saturday said that while recognising there were “different views” among members, G20 leaders wanted to highlight the “human suffering” being caused by the decision of Mr Putin, who stayed away from the forum in India, to blockade Ukrainian grain.
The G20 called for the reimplementation of the Black Sea Grain Initiative, which allowed safe passage for cargo ships transporting food from Ukraine’s southern ports and which the Kremlin collapsed in July, to be re-established and urged for attacks on grain stores to cease.
The wording was described as a “good and strong outcome” by Mr Sunak but there was some concern among summit watchers that some of the language around the Ukraine conflict had been watered down, potentially in a move designed to appease China.
During their meeting, Mr Sunak and Mr Modi demonstrated their cordial relationship with a hug and back slapping before talking for at least 15 minutes.
Mr Sunak told the Hindu nationalist leader that his daughters had followed India’s moon landing and that “everyone was buzzing” about the mission’s success.
Following the talks, Mr Sunak confirmed, having been lobbied on the issue by MPs, that he raised the issue of detained Briton Jagtar Singh Johal, a Sikh blogger who is at risk of the death penalty in India.
The press had uncharacteristically restricted access to the opening exchanges of the bilateral between the premiers, with the summit being tightly controlled by its Indian hosts.
The area around the Bharat Mandapam venue has been largely locked down, with independent businesses told not to open and normally busy roads left empty of the usual noisy rickshaw, motorbike and car traffic.
The Prime Minister has enjoyed extensive media coverage in India about his return to the country of his heritage, with locals also keen for a photo opportunity with his wife Akshata Murty, the daughter of NR Narayana Murty, the billionaire co-founder of Indian IT giant Infosys.
No 10 confirmed the Prime Minister’s parents and his in-laws are currently on holiday together in Bangalore, a city in southern India, but said it was coincidental that it coincided with when their children were at the G20.