In a television interview, Cameron said search engines must block results for searches using blacklisted keywords to stop Internet users accessing illegal images.
Evidence in two recent high-profile child murders in Britain has shown that the killers accessed online child pornography. Although search companies have pledged to help remove images from the Internet, Cameron says he wants them to go further.
"I have a very clear message for Google, Bing, Yahoo and the rest. You have a duty to act on this - and it is a moral duty," Cameron was due to say in a speech on Monday, according to an advance text, demanding that the companies report back to him in October on their progress.
Cameron also said the government was ready to introduce new laws if search engine providers did not offer enough cooperation.
Last week, U.S. authorities said they had arrested 255 people suspected of sexually exploiting children online in a cross-border operation involving eight other countries.
In June, Google donated around 3 million pounds to combat the problem, including 1 million pounds to the Internet Watch Foundation, a group committed to ridding the Internet of child pornography.
"We have a zero tolerance attitude to child sexual abuse imagery. Whenever we discover it, we respond quickly to remove and report it," a Google spokesperson said.
Bing, owned by Microsoft Corp, said it would support education and deterrence campaigns and that it was working with the British government to determine the best industry-wide approach to tackle illegal content.
Yahoo was not immediately available for comment.
© Thomson Reuters 2013
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