Boris Johnson has added his voice to suggestions the Communications Data Bill could be revived following the murder of soldier Lee Rigby.
The London mayor said it was "too early" to say whether the bill - dubbed a "snoopers' charter" by critics - would have prevented the attack.
But he said police arguments for the proposed law were "pretty compelling".
The bill, allowing the monitoring of all UK citizens' internet use, was dropped after Lib Dem opposition.
But according to The Independent newspaper, Home Secretary Theresa May is coming under pressure from senior figures in the Conservative Party to revive it.
'Stone Age behaviour'
Asked whether it was time to progress with the "snoopers' charter", given everything that has happened, Mr Johnson said: "It's much too early for us to say whether it would have been of any use at all in this particular case.
"Over the past year the police have made powerful representations to me of the usefulness of this ability. I must say their arguments have been pretty compelling."
Drummer Rigby, 25, was murdered on a street in Woolwich, south-east London on Wednesday afternoon.
The UK's security services face a Commons inquiry after it was confirmed the two men arrested over the murder were known to MI5.
Communities Secretary Eric Pickles suggested the Communications Data Bill could be re-examined, once the inquiry had been completed.
But he gave no indication the government was planning immediate action.
He told BBC News: "I've seen nothing in the reports so far that suggests these communications powers would have made any difference whatsoever.
However, the prime minister has announced an inquiry, clearly that inquiry will look at all aspects and some time we may come back and re-look at this.
"But it is perhaps too tempting to think there is an instant solution. This is extraordinarily primitive, almost Stone Age behaviour."
Speaking on Newsnight on Wednesday both Lord Carlile, the Lib Dem former independent reviewer of terror laws, and Labour's Former Home Secretary John Reid urged the government to consider introducing the Data Communications Bill.
Prime Minister David Cameron has previously warned that scrapping the plans would put national security at risk by making it harder to bring terror suspects and other criminals to justice.
But Deputy Prime Minister Nick Clegg blocked the change, insisting storing records of internet use for a year and allowing police and security service access to a vast "treasure trove" of information was neither workable nor proportionate.