Parliament's Intelligence and Security Committee said it would probe whether Britain's laws on intercepting private communications, drafted well over a decade ago, are still adequate in the Internet age.
Snowden, a former NSA contactor, earlier this year disclosed details of the vast communications-monitoring programs carried out by the American agency and its international counterparts, including Britain's GCHQ.
The revelations sparked an international debate about the scale of surveillance and the erosion of privacy in the digital age.
An earlier investigation by the parliamentary committee concluded in July that GCHQ did not use the NSA's PRISM information-gathering program to get around British restrictions on domestic espionage.
But civil liberties groups have demanded a wider inquiry into the scale of Web surveillance.
Committee chairman Malcolm Rifkind acknowledged Thursday that there was a need for "an informed and responsible debate" about the balance between individual privacy and collective security.
He said in a statement that the committee would examine classified information, but also accept written submissions from the public, "to ensure that the committee can consider the full range of opinions expressed on these topics."
"Once it has considered those written submissions it will also hold oral evidence sessions, some of which it expects to hold in public," he said.
Shami Chakrabarti of the rights group Liberty said it was unclear whether the inquiry would seek the truth or be "a tactical whitewash to calm public concern."
"It's certainly significant that the committee feels compelled to dig a little deeper, but that's no substitute for much broader public and political debate," she said.