India's current Prime Minister, Manmohan Singh, has phoned his opponent Narendra Modi to congratulate him on the BJP party's victory in the Indian elections.
With early results coming in, the nationalist BJP is set for a landslide victory over Dr Singh's Congress Party.
David Cameron played down suggestions that he was involved in a “frosty meeting” with Indian Prime Minister Manmohan Singh due to tensions over several issues.
Cameron told ITV News: “We have met many times, we get on very well.
"We both, as you’ve heard, share this view that there should be a very special partnership between Britain and India in the years ahead."
He added: “But like any good friends and any two countries that have a good and strong relationship, we raise issues of concern.
"There are things I want the Indian government to do: make it easier for insurance, banking and retail firms to invest in India.”
The Prime Minister has met Sonia Gandhi, President of the Indian National Congress party, at her residence in New Delhi.
The Prime Minister had the unusual pleasure of being greeted by hundreds of screaming women when he visited a women's college in the Indian capital Delhi today.
The applause may have had more to do with the Bollywood star accompanying him, but the students listened attentively to what he had to say.
India's Prime Minister took the opportunity of a meeting with David Cameron to raise his concerns about a deal between Anglo-Italian helicopter firm AgustaWestland and the Indian air force.
Authorities in India are concerned that the £480 million contract to supply the air force with military helicopters may have broken corruption and tax fraud laws.
It follows the arrest in Italy of two executives from the firm and its parent company Finmeccanica.
Mr Cameron said it was a matter for Italian investigators, since Finmeccanica is an Italian firm, but that Britain would cooperate with any requests for information.
The Prime Minister found himself in the midst of a crowd of screaming girls when he appeared alongside Bollywood superstar Aamir Khan at the Janki Devi Memorial College in Delhi.
The film heartthrob is also a Unicef ambassador for child nutrition and the patron of a women-only taxi service in the city.
Khan introduced Mr Cameron to some of the Sakha Cabs workers, who are trained in car mechanics and self-defence at the college.
The Prime Minister has said Britain and India are "on track" to double trade to £23 billion by 2015. Speaking after a meeting with his India counterpart Manmohan Singh, he said:
He also added that he wanted to see "rapid progress" towards the completion of an EU-India free trade agreement.
David Cameron and India's Prime Minister Manmohan Singh discussed measures to increase the flow of people between Britain and India during a joint press conference today.
Mr Cameron announced the launch of a same-day visa service for business employees travelling to the UK, saying "we want you to come to our country quickly and invest in our country".
India's Prime Minister Manmohan Singh has told David Cameron he has "very serious concerns about unethical means" used to secure a deal between Anglo-Italian helicopter firm AgustaWestland and the Indian air force.
Mr Cameron has said that the UK will respond to any requests for information, and that he is glad that Italian authorities are investigating the matter.