Theresa May has announced new passport and visa schemes to make it easier for businessmen from India to come to the UK.
A small number of "high net worth" individuals and their families will be allowed access to the Great Club arrangement to smooth the process of applying for a visa.
Meanwhile, thousands of executives will be able to fast track through UK airports by taking advantage of the Registered Traveller Scheme.
The Prime Minister has, however, signalled to India that she will not be pressured into easing restrictions for student and work visas, saying there is already a "good system" for applications.
Mrs May has come to India as part of a 33-strong business delegation, with the aim of reducing barriers to commercial links, as well as paving the way for a free trade deal when Britain leaves the EU.
But Indian Prime Minister Narendra Modi is expected to use the talks to put pressure on May to relax visa rules.
Indian government spokesman Vikas Swarup said: "In the last five years or so, the number of Indian students enrolling in UK universities has gone down by almost 50% - from around 40,000 to about 20,000 now. This has happened because of restrictions on post-study stay in the UK.
"We will continue to raise our concerns regarding mobility with the UK. Mobility of people is closely linked to free flow of finance, goods and services."
Asked whether she was considering freeing up visa rules, Mrs May told reporters: "The figures show that we issue more work visas to India than (to) the US, Australia and China put together. Nine out of 10 visa applications from India are already accepted.
"So we have, I believe, a good system."
Prior to her meeting with Mr Modi, Mrs May was due to meet Indian business leaders at a technology summit on Monday.