Gordon Brown has announced a new package of development aid for India, worth ?825m over the next three years.
The funding is expected to target areas such as the eastern state of Bihar, one of India's poorest.
Mr Brown was speaking at the start of a two-day visit to India intended to improve business ties and co-operation in the fight against terrorism.
He is using his visits to China and India to promote better trade agreements with the UK.
Upon his arrival in Delhi, Mr Brown toured a project designed to boost the role of women in society with his wife Sarah.
He said: "We are inspired by the young girls here who are telling us of their aspirations for the future.
"Women are changing India and are the driving force of change for the future."
Mr Brown said that of the new aid package, ?500m will be dedicated to health and education.
He said the money would be used to train 300,000 new teachers and build 300,000 new classrooms, meaning 4m more children would receive an education.
The prime minister is also being accompanied on his trip by a group of academics from colleges such as Oxford University and Imperial College London, who are hoping to encourage stronger links between British and Indian universities.
Mr Brown and his entourage flew in to the Indian capital New Delhi on Sunday from the Chinese city of Shanghai.
The delegation includes senior industry figures, including CBI director general Richard Lambert and Virgin Group's Sir Richard Branson, and double Olympic gold medallist Dame Kelly Holmes.
Mr Brown has also called on the Indian authorities to play a greater role in the fight against terrorism, saying he wants to see cross-religion co-operation on the issue.
He told the BBC there needed to be "greater co-operation between the major countries in the fight against terrorism" and said China, Pakistan and India all had a part to play in rooting out those responsible.
He called on India to join the Financial Action Taskforce, an inter-governmental body which helps combat money laundering and terrorist financing.
Greater co-operation was also needed on what to do in crowded places, such as security at airports and ports, he said.
He added that extremist ideologies needed to be fought and that co-operation across religions was "going to be very important for the future".
"So what we need now is a comprehensive action plan, if you like a global action against terrorism," he said.
Save the Children said the British aid package must reach India's excluded children.
Shireen Vakil Miller, of Save the Children India, said: "There is a real need to examine how children are looked at in a country that allocates less than 5% of its GDP to children, despite the fact they make up almost 40% of the population."