"In the last 12 months, there have been significant developments in the legal process following the 2002 Gujarat riots, including convictions in a number of high profile cases," Mr Cameron told The Eastern Eye, a weekly published by the Garavi Gujarat Group of newspapers.
"We believe that closer engagement with Gujarat, including Chief Minister Narendra Modi, is now the best way to achieve our wide-ranging objectives there - including on human rights - and ensure that the UK can provide a full and consistent range of services across India," the British Prime Minister said.
Asked whether the UK will issue a visa to Modi if he wins the general elections in 2014 for BJP, Mr Cameron said, "Any visa application is assessed on its merits. We are committed to a strong bilateral relationship with India, and that includes welcoming the Indian Prime Minister here for bilateral meetings."
Last week, Mr Modi was named as the Bharatiya Janata Party's prime ministerial candidate.
Although many western nations including Britain and the US distanced themselves from Mr Modi in the immediate aftermath of the 2002 riots, there has been a shift in their position in the past year. (Read: US should find ways to engage with Modi, says former diplomat)
In March this year, Britain's Foreign Office Minister Hugo Swire met Mr Modi in Gujarat, saying it was "a logical next step" in Britain's relations with the Indian state.
"I am confident that active engagement is the best way to pursue British interests in Gujarat. This includes support for the British nationals in Gujarat, for the large Gujarati community in the UK, for human rights, and good governance," Mr Swire had said at the time.
It came on the back of lobbying by business groups, who sensed investment opportunities in the state and were keen to tap into the bond British Gujaratis have with their homeland.
"There were arguments made privately for the UK government to start changing its stance in Gujarat," said Patricia Hewitt, chair of the UK India Business Council.
Barry Gardiner, MP for Brent North and chair of the Labour Friends of India, recently invited Mr Modi to the UK.