The state of emergency has been in place since the Paris attacks in November, and the extension would see the measures — which give the police extra powers to carry out searches and place people under house arrest — remain in place until the end of January 2017.
It is the fourth time that parliament has proposed prolonging the state of emergency, and the move now needs to be approved by the Senate.
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Hollande's Socialist government has been under heavy criticism from the right for its response to the slew of extremist attacks.
The fact the president was open to the six-month extension was seen as a concession to opposition Republicans who have demanded that the state of emergency be maintained through to the end of the year.
With elections due next year, the political unity seen after last year's attack on satirical magazine Charlie Hebdo has evaporated.
Interior Minister Bernard Cazeneuve has defended the government, saying it has bolstered security notably by sending thousands of troops into the streets.
French Prime Minister Manuel Valls warned Tuesday that the country must be prepared for more deadly attacks and will have to "learn to live with the threat".
But the Socialists have also said they will draw the line at some of the opposition's more controversial demands.
Republicans leader and former president Nicolas Sarkozy, eyeing another run for the top job next year, has called for anyone showing signs of being radicalised to be forced to wear an electronic tag, placed under house arrest or kept in a detention centre.
While some on the right think the six-month extension is not sufficient, there are also critics on the left concerned about civil liberties who say even with the state of emergency in place an attack occurred.
"We can't lock people up on the basis of mere suspicion, or suspicion of suspicion," minister for parliamentary relations Jean-Marie Le Guen said Tuesday.
Valls hit out at the Republicans number two, Laurent Wauquiez, after Wednesday morning's National Assembly vote.
"While this government is in place in France, there will be no detention of suspects for an indeterminate duration," he said.
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