"I am delighted Cameron will be invited to a special session of the European Parliament," Liberal Group leader Guy Verhofstadt said in a tweeted message after MEPs agreed to ask assembly head Martin Schulz to approach Cameron.
"The European Parliament is nothing for Cameron to be afraid of," said Verhofstadt, who has pressed repeatedly for the prime minister to come to Brussels and explain his position.
"Let's hope Cameron seizes this opportunity to outline transparently his demands for a renegotiation of UK's membership," he added.
"The result (of the MEP meeting) is for President Schulz to call Cameron to sound out (the) possibilities," a press officer said.
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Cameron won re-election earlier this year promising voters a straight 'in-out' vote on Britain's EU membership by 2017.
He made a first case to EU leaders at a summit in June, setting off the negotiating process, with the issue to be taken up again at a December summit after.
Critics say London has been very short on specifics but Cameron says he wants curbs on welfare payments to migrants and an opt-out on its drive towards ever closer union.
Recent polls have shown a majority of Britons want to stay in the EU although the outcome is expected to be tight.
Most EU states have reacted cautiously to Cameron's drive, agreeing with some of his complaints about the EU but also expressing the hope Britain will stay in the 28-nation bloc.