The Investigatory Powers Bill, dubbed the ‘snooper's charter’ by critics, has been approved by MPs at second reading by 281 votes to 15, majority 266.
But senior Conservatives have urged Home Secretary Theresa May to improve controversial proposed spying powers as they cleared their first Commons hurdle.
Former Conservative minister David Davis told MPs there are "many other significant flaws" in the Bill which must be put right, including the lack of measures to protect people's privacy.
He also labelled powers enabling intelligence agencies to bulk collect data as "potent", noting they allow "industrial scale exploitation of phones and computers".
Davis said MPs must question if such powers are effective, adding they have been curbed in the United States as they are not considered essential in preventing terrorist attacks.
He believes the Bill must be drafted "incredibly precisely", arguing that its current language "is designed to confuse".
"The previous home secretary (Conservative MP Ken Clarke) and I were talking about this, we both had trouble understanding 250 pages of this Act as it stands,” he said
Labour and the SNP abstained from the vote and warned they could vote against the government at future stages unless it ironed out problems with the Bill.
The Liberal Democrats, who oppose the Bill in principle, helped to force the vote.
The position of opposition parties and some of the unease on the Tory backbenches could force the government to grant concessions as the Bill passes through the Commons.
Ken Clarke warned that justifications for using the intrusive spying powers on grounds of national security or protecting economic well-being could be misused.
"The devil is in the detail and actually there are some quite important points where we should still be questioning,” he said.
"It is true that there is a vast amount of activity under the general title of economic well-being.
"I've known some very odd things happening under that head. National security can easily get conflated with the policy of the government of the day and I don't know quite how you get the definition right, but it's no good just dismissing that point."
Government sources recently said that a revised version of the Bill will not oblige technology firms to weaken security by undermining encryption systems.