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LONDON — Popular messaging services like Snapchat and WhatsApp are in the cross hairs in Britain.

That was the message delivered on Monday by Prime Minister David Cameron, who said he would pursue banning encrypted messaging services if Britain’s intelligence services were not given access to the communications.

The statement comes as many European politicians are demanding that Internet companies like Google and Facebook provide greater information about people’s online activities after several recent terrorist threats, including the attacks in Paris.

Mr. Cameron, who has started to campaign ahead of a national election in Britain in May, said his government, if elected, would ban encrypted online communication tools that could potentially be used by terrorists if the country’s intelligence agencies were not given increased access. The reforms are part of new legislation that would force telecom operators and Internet services providers to store more data on people’s online activities, including social network messages.

“Are we going to allow a means of communications which it simply isn’t possible to read?” Mr. Cameron said at an event on Monday, in reference to services like WhatsApp, Snapchat and other encrypted online applications. “My answer to that question is: ‘No, we must not.’ ”

Mr. Cameron said his first duty was to protect the country against terrorist attacks.

“The attacks in Paris demonstrated the scale of the threat that we face and the need to have robust powers through our intelligence and security agencies in order to keep our people safe,” he added.

Any restriction on these online services, however, would not take effect until 2016, at the earliest, and it remained unclear how the British government could stop people from using these apps, which are used by hundreds of millions of people worldwide.

Mr. Cameron’s comments are part of a growing debate in Europe and the United States over whether Internet companies and telecom providers must cooperate fully with intelligence agencies, who have seen an increased use of social media by groups like the Islamic State, also known as ISIS or ISIL.

After the Paris attacks, European leaders, for example, called on Internet service providers to report potentially harmful online material aimed at inciting hatred or terror.

“We are concerned at the increasingly frequent use of the Internet to fuel hatred and violence and signal our determination to ensure that the Internet is not abused to this end,” European Union politicians said in a joint statement.

Last year, European officials also met with some American tech giants, including Microsoft and Twitter, to discuss how companies could control what was published on their networks, though the companies have resisted greater oversight by intelligence services.

Yet in a sign that tech companies are coming under increased scrutiny, British lawmakers blamed Facebook in November for failing to tell the country’s authorities about specific online threats made by two men, who later killed a soldier in London in 2013.

Facebook declined to comment on the accusations, though said that it had taken measures to prevent terrorists from using the social network.