He said: "We cannot tolerate in any sense the idea that this country [Pakistan] is allowed to look both ways and is able, in any way, to promote the export of terror, whether to India or whether to Afghanistan or anywhere else in the world."
Though his comments were likely to be welcomed in India, which often accuses Islamabad of harbouring armed groups, Pakistan's reaction has been quick and angry.
Basit strongly denied any Pakistani links with terror groups and defended Islamabad's role.
"Britain knows full well as to how Pakistan, particularly the ISI [the Pakistani intelligence service] has been extending help and assistance to Britain in thwarting so many terrorist plots in Britain.
"The ISI has been extending help and assistance to Britain in thwarting so many terrorist plots."
Pakistani foreign ministry spokesman
"They know the effectiveness of the ISI and our constructive and positive role in Afghanistan so we do not find any reason whatsoever for such remarks."
Earlier, 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.
He also refuted renewed criticism of Pakistani intelligence servicesover its alleged ties to Taliban, following revelations by Wikileaks, the whistle blower website.
The site leaked US government documentssuggesting links between Pakistan's security services, the Taliban and other groups operating in Afghanistan.
"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.
But Ian Black, the Middle East editor for Britain's Guardian newspaper, said Cameron's comments were an attempt to send clear messages about British foreign policy.
"I think what you have here is a new prime minister who is anxious to create a sense of his own competence to establish his presence on the world stage," Black told Al Jazeera.
"And by his own admission he likes to use clear, strong language.
"Having said that he's perfectly capable of being diplomatic and not saying things that would upset his hosts ... but I think Cameron is trying to send clear messages."
Cameron's comments came during a two-day visit to India, which is aimed at improving bilateral trade between London and New Delhi.
He was meeting Manmohan Singh, the Indian prime minister, on Thursday.
Rahul Roy-Chaudhury, a South Asia expert for the International Institute for Strategic Studies in London, said Cameron's comments in India were made "to please the host nation".
"He's very keen to boost the bilateral ties and it's very clear that this can't only take place on the base of trade and economic issues but needs a security dimension," he told Al Jazeera.
"It is significant that he has made these remarks on Pakistan in India during a state visit as opposed to making them in London.
"But they still don't go far enough in terms of the Indian government's perspective. After all he has not talked about any complicity of elements of the Pakistani government in terrorism, an allegation that India strongly supports."
Cameron is scheduled to meet Asif Ali Zardari, the Pakistani president, in Britain next week.