He believes a “zero-tolerance” stance against radical Islam is needed to stop communities becoming “degenerate”.
Mr Gabriel wants the proposed crackdown to focus on Salafism – an ultra-conservative branch of Islam based on Sharia law.
Salafist mosques must be banned
“Those who encourage for violence do not enjoy the protection of religious freedom.
“If we are serious about the fight against Islamism and terrorism, then it must also be a cultural fight.”
The Tunisian, who was known to authorities, ploughed a lorry into a packed Christmas market in the German capital.
He was discussed seven times among security chiefs before the attack – but they decided he did not present a clear and present danger.
Merkel admits Islamist terrorism is the biggest threat facing Germany
But she insisted the country would remain “free, considerate and open”.
She said: “Our values are the opposite of the hate-filled world of terrorism and will prove stronger than it. Together we are stronger.”