Pakistan's High Commissioner to Britain, Wajid Shamsul Hasan, said people in Pakistan were "really hurt" by Mr Cameron's remarks and called on him to "make amends".
But in an interview with Sky's political editor Adam Boulton, Mr Cameron said: "I think you should say what you think, and be frank and clear.
"It's not acceptable that there are still terrorist groups working in Pakistan.
"We need to work with the government there to shut them down.
"There is action being taken, but we need to see more."
The Prime Minister told Boulton Britain needed a "gritty, realistic, hard-headed foreign policy".
"It's all part of a common agenda towards a strong economy," he said.
"It's a signal to the rest of the world that Britain wants to trade again, invest again, make things again."
He also defended his charm offensive in India, saying: "It's not a question of humbling ourselves.
"This is a jobs mission.
"India is one of the fastest-growing economies in the world - one of the stars of the future.
"There is an opportunity for all industries to grow their businesses by investing in India.
"A strong relationship is necessary to help create jobs at home."
Mr Cameron is meeting a series of senior politicians on the final day of his trip.
He will have talks with President Pratibha Patil and Congress president Sonia Gandhi, among others.
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