The comments were likely welcomed in India, which has accused Pakistani intelligence officials of harbouring and abetting groups such as Lashkar-e-Taiba, which India has blamed the 2008 attacks in the city Mumbai.
But Pakistan was swift to condemn the comments, accusing the UK of "kicking their own friends".
Wajid Shamsul Hasan, Pakistan's high commissioner in London, told Al Jazeera that he had received hundreds of calls from Pakistanis, who offered "a very sharp reaction" to Cameron's comments.
"I think Cameron will review his statement, clarify his position, because we need to be supported not criticised for what we are doing," Hasan said.
Cameron's comments came after WikiLeaks, the whistle blower website, leaked US government documents accusing Pakistan's security services, the ISI, of collaborating with the Taliban and other groups operating in Afghanistan.
"We should be very, very clear with Pakistan that we want to see a strong, stable and democratic Pakistan," Cameron said.
"It should be a relationship based on a very clear message: that it is not right to have any relationship with groups that are promoting terror."
But Hasan condemned the claims made in the leaked US documents, calling them "untrue" and saying "they have not given us any solid evidence".
"ISI was one of the conduits used by the CIA and other agencies to raise these Taliban, these mujahidin, to fight the Soviets in Afghanistan. Only [the] ISI can't be blamed for it," he said.
Vikas Pota, a political analyst in London, told Al Jazeera that Cameron's speech will be good for business, the primary purpose of his visit to India.
"By making the speech that he did [Indian prime minister Manmohan] Singh will welcome him [Cameron] with open arms" when they meet in New Delhi, Potas said.
Bilateral trade between Indian and Britain was worth than $13bn last year.
Cameron hopes to increase that number with a series of defence deals, as he tours India with a large delegation of British business and political leaders.