DERBY North MP Chris Williamson says it is time to consider allowing anti-terrorist police to "snoop" into people's private lives in a bid to stop attacks.
The Labour politician said he did not necessarily disagree with comments made by Theresa May that it is "essential" intelligence agencies have greater access to communications data.
The Home Secretary said it would give law enforcement agencies the "tools they need" to track down terrorists before they can launch attacks following the murder of off-duty soldier Lee Rigby in Woolwich.
The killing has re-ignited the debate over a so-called snooper's charter, which was dropped from the Queen's Speech earlier this month.
The plans could have given officials the power to spy on the public's every internet click and Facebook visit.
Mr Williamson said giving agencies greater spying power was something that needed to be "looked at".
He said: "Clearly, we do need to look at what more can be done to prevent such a horrendous incident from occurring again.
"I would like to see all the options looked at again to see if more can be done to prevent a repetition of this tragedy."
Asked whether he believed agencies should be allowed to access the public's private messages on social media sites, Mr Williamson said: "That's the sort of detail we need to look into. I think we need to explore all options."
Mrs May also said "thousands" of people were at risk of radicalisation and that extremists should not be allowed to appear on TV.
On this point, Mr Williamson said he disagreed with the Home Secretary.
"We went down this road with the IRA and that wasn't successful," he said. "We need to win people's hearts and minds and prevent them from being radicalised but simply banning extremists from being on TV doesn't win the battle in the end."
Deputy Prime Minister Nick Clegg vetoed the inclusion of the controversial Communications Data Bill in the Queen's Speech.
Plans in a draft bill published last year would have given agencies including the police and intelligence services access to information including individuals' web browsing history and social media messages.
Yesterday detectives arrested a 50-year-old man on suspicion of conspiracy to murder in South East London.
The arrest was the tenth officers have made over the murder of the 25-year-old, who was hacked to death in the street by Islamic extremists last week.
Committee members from Derby's Jamia Mosque have denounced the murder of Drummer Rigby.
A spokesman for the mosque said: "The actions have no place in any teachings of Islam. As Muslims, we are disgusted by these outrageous acts which are nothing less than inhumane and barbaric.
"Many attendees have expressed their shock and horror.
"The community is in a sombre mood."
Tributes to the dead soldier have been laid at the war memorial in Derby's Market Place. Laying flowers, John Marsh, from Ripley, said: "It's good to see the tributes locally – we are taking a closer look while we are here."
