Paris attacks: France mobilises 115,000 security personnel
Mr Cazeneuve said 128 more raids on suspected militants were carried out. French air strikes also hit Islamic State in Syria overnight.
IS has said it carried out the attacks on bars, restaurants, a concert hall and a stadium in which 129 people died.
A huge manhunt is under way for one of the suspects, Salah Abdeslam.
He is believed to have fled across the border to his native Belgium. Belgian police have released more pictures of the wanted man.
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Belgium's government has raised its terror threat level because of the failure so far to arrest Abdeslam. Tuesday's football match between the national team and Spain has been cancelled as a result.
Mr Cazeneuve said: "We have mobilised 115,000 police, gendarmes and military over the whole of our national territory to insure the protection of French people."
He vowed to boost funding for police equipment, which he said had fallen by 17% in 2007-12.
The interior minister added that 128 raids on suspected Islamist militants had been carried out overnight on Monday to Tuesday. More than 160 raids were made earlier on Monday, with 23 people arrested and dozens of weapons seized.
French media reported that during raids police found a safe house used by the attackers in Bobigny, a suburb of Paris.
Meanwhile France has evoked a previously unused clause in the Treaty on European Union obliging other member states to provide it with "aid and assistance by all means in their power".
Within minutes, EU foreign policy chief Federica Mogherini said that all 28 member states had offered "full support and readiness to provide all the aid and assistance needed".
The measures came as US Secretary of State John Kerry visited Paris. Speaking on Monday, he described IS as "psychopathic monsters".
After meeting French President Francois Hollande on Tuesday, he said everyone understood that after Paris and other recent attacks "we have to step up efforts to hit them at the core" and improve border security.
Mr Hollande is due to fly to Washington and Moscow next week for talks with US and Russian leaders.
The attacks in Paris - which also left more than 400 people wounded, some critically - have galvanised Western countries in their campaign against the so-called Islamic State.
UK Chancellor George Osborne is due to say in a speech on Tuesday that IS is trying to develop the ability to launch deadly cyber-attacks on the UK
During a visit to the GCHQ listening station in Cheltenham, he is to announce that the UK's investment in fighting cybercrime will double.
President Hollande told a rare joint session of the French parliament on Monday that he would table a bill to extend for three months the state of emergency declared after the attacks. Parliament will vote on the measure on Wednesday.
According to Prime Minister Manuel Valls, intelligence services have files on 10,500 individuals who have been radicalised to a greater or lesser extent.
Seven people were detained in Belgium over the weekend, two of whom were charged on Monday with "participating in a terrorist attack".
The other five were later released, including Mohammed Abdeslam, the brother of two suspects - Brahim Abdeslam, killed during the attacks, and Salah Abdeslam.
Suspected Paris attackers
Source: BBC News