LeT has been blamed for attacks on Mumbai in 2008, which left 166 people dead and further derailed peace talks between India and Pakistan.
Singh on Thursday called on Pakistan to make equal efforts to eliminate fighters operating in western border areas near Afghanistan and the eastern border with India.
"I sincerely hope that the government of Pakistan will honour its commitment given to us on a number of occasions that Pakistani territory will not be allowed to be used for terrorism," he said.
"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"
Middle East editor
at the Guardian
Pakistan has come under concerted pressure this week after leaked US military documents alleged links between Pakistan's ISI intelligence services and Taliban fighters in Afghanistan.
Islamabad has strongly criticised Cameron, who is on a two-day visit to India aimed at improving bilateral trade between London and New Delhi, for his remarks.
Abdul Basit, a Pakistan foreign ministry spokesman, said the prime minister seemed to have based his comments on the leaked US documents, which he called "biased and self-serving".
"We are obviously disappointed at these comments because these are not coming from any original source, rather biased sources and I would say not even raw intelligence but disinformation against Pakistan," he told Al Jazeera.
In his comments on Wednesday, Cameron had said that Islamabad should know "that it is not right to have any relationship with groups that are promoting terror".
"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," he said.
'Pleasing his hosts'
Rahul Roy-Chaudhury, a South Asia expert for the International Institute for Strategic Studies in London, said Cameron's comments were made "to please the host nation".
|Cameron, left, is on a two-day visit to
promote trade with India [AFP]
"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."
Pakistan's Basit strongly denied any Pakistani links with terrorist groups and defended Islamabad's role.
"Britain knows full well as to how Pakistan, particularly the ISI has been extending help and assistance to Britain in thwarting so many terrorist plots in Britain," he said.
"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," Hasan said.
Ian Black, the Middle East editor for Britain's Guardian newspaper, said Cameron's comments were an attempt to send out clear messages about UK 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," he told Al Jazeera.
"And by his own admission he likes to use clear, strong language."
Cameron is scheduled to meet Asif Ali Zardari, the Pakistani president, in Britain next week.