The programme, which was uncovered through the leaking of a number of secret documents to the Guardian and the Washington Post this week, allows the government to secretly mine personal data of the users of a number of tech giants such as Google, Microsoft and Apple.
On Friday, it emerged that the British security communications hub GCHQ also used the spying programme to gather information on British citizens.
Davis, who was shadow home secretary from 2003-2008, has revealed that he believes the upper echelons of government, including home secretary Theresa May and foreign secretary William Hague, could well have known about the programme.
The MP told Sky News on Saturday that he suspected the two knew and that “presumably they at least would have had to sign an authorisation for this to take place.”
Davis added that if current reports are correct, “it is actually quite a scandal” as it allowed the state to “spy on who they like”.
On Friday, had Davis said that: “The issue is pretty simple. Whether this monitoring is happening abroad or not, in any event the individual concerned may well be in the UK when he sends the email.”
Davis’ concerns were echoed by the shadow home secretary Yvette Cooper and shadow foreign secretary Douglas Alexander.
Alexander told Sky News on Saturday that: “Our intelligence agencies do vital work to keep our country safe from harm, but it is also vital that they operate within a framework of legality and accountability.
“These reports have raised serious public concern, so I am now calling on the Foreign Secretary, William Hague, to come to the Commons on Monday to make an urgent statement to MPs.
“In that statement he must explain the Government’s position and tell MPs how the Government will work with the Intelligence and Security Committee to address these public concerns.”
“The Government also needs to set out clearly what legal framework governs the UK relationship with the Prism programme, what role Ministers play, what the safeguards and scrutiny are. They need to explain how this relates to long standing legal requirements for warrants and inspection by the Intercept Commissioner.”
Leaked documents were said to show that the British agency, based at Cheltenham, had generated 197 intelligence reports through the system in the 12 months to May 2012 – a 137% increase on the previous year.
GCHQ officials will now go before the International Security Committee to detail how and what to extent it used the spy programme. GCHQ refused to comment directly on the report, but in a statement it insisted that it operated within a “strict legal and policy framework”.
“GCHQ takes its obligations under the law very seriously,” the statement said.