Rishi Sunak said he "won't rush" into a UK trade deal with India, as he arrived in the country for a summit of G20 leaders.
The UK prime minister said he would not set a deadline for negotiations, which began early last year, to conclude.
Expectations have been growing an agreement could be struck before the end of the year.
Mr Sunak told reporters that progress has been made, but "we're not there yet".
India would be the biggest country yet to strike a trade agreement with the UK since it left the European Union's trading system in 2021.
Mr Sunak is in India for a meeting of the G20, with leaders of the world's largest economies.
A UK-India deal is not on the agenda, but Mr Sunak is expected to discuss progress so far with his Indian counterpart Narendra Modi on the sidelines of the summit this weekend.
He was given a colourful welcome on his arrival in Delhi on Friday, with traditional dancers and music greeting him as he stepped off his plane.
He later met local school children with his wife Akshata Murty, the daughter of the billionaire co-founder of Indian IT giant Infosys.
Trade negotiations between the two countries began in January last year and have stretched across twelve rounds, with the next round scheduled for later this month.
Key interests for the UK side include lowering India's high import tariffs on British-made cars, dairy products and drinks including Scotch whisky.
The UK has been keen to get India to allow greater access to UK financial and other professional services firms to operate in India.
But Mr Sunak is facing pressure not to relax UK visa rules for Indian nationals, amid reports that Home Secretary Suella Braverman has concerns it could hamper efforts to bring down net immigration.
Ahead of the summit, Downing Street ruled out issuing more student visas to get a deal done, with the PM's spokesman adding it had "no plans to change our immigration policy".
India's high commissioner to the UK has insisted it is not looking for more visas, although he added his country wanted Indians studying in the UK to be able to do work experience after they graduate.
Speaking to Times Radio, Vikram Doraiswami added that Indian students were paying "significant money" in fees to UK universities and wanted rights "permissible to other nationalities".
He said India was also looking to make it easier for companies based in both countries to temporarily transfer workers as part of a deal, and for Indians who work in the UK for short periods to be able to transfer their pension contributions back to India.
"We're not asking for migrants to be able to come here," he said, adding: "That's been in your press, not in ours".
Diwali deadline missed
Former Prime Minister Boris Johnson set a deadline to get a deal with India "done" by October last year, in time for Diwali - but he was ousted from office in July and the deadline came and went.
There have been reports that Mr Modi is keen to strike a slimmed-down deal to reduce import taxes, with some easier access for services firms, ahead of election next year.
Speaking to reporters, Mr Sunak said since taking office last year he had "taken the time" to ensure international negotiations "work for the British people".
"I won't rush things for the sake of it until they're right for us," he added.