He announced extra personnel, equipment and surveillance powers for the police.
But he rejected banning the public wearing of the burka (the Islamic full veil). And he resisted pressure to ease medical confidentiality.
Some of his conservative Christian Democrat (CDU) colleagues have urged a burka ban but Mr de Maiziere said it would be "problematic" and "you cannot ban everything that you reject".
Mr de Maiziere was responding to recent attacks linked to militant Islamists. Two terror attacks by Islamist migrants shocked Germany last month - in Wuerzburg and Ansbach.
"I propose that German citizens who are fighting with terror militias in other countries, and take part in combat operations there, if they have a second nationality - and only then - they would lose German citizenship," he told a news conference.
There was a move in France recently to deprive jihadists of their French citizenship, but it did not get through parliament.
"My proposals are limited to the points that can lead to more security rapidly," Mr de Maiziere said.
One of the new measures is to make "promoting terrorism" a criminal offence.
The security issue has become intensely political, as the country prepares for general elections next year and earlier regional elections.
German media report that the centre-left Social Democrats (SPD) - the CDU's coalition partners - strongly oppose any general ban on dual citizenship. The Greens are also against the idea.
The duty of doctors to respect patient confidentiality is enshrined in the German constitution. And German privacy laws are very strict.
But Mr de Maiziere said he would meet senior doctors to discuss how they could more easily tip off police when they suspected a patient was a terror risk.
In three major cases the perpetrators were found to have been mentally unstable:
· The Ansbach bomber who killed himself and wounded 15 others at a music festival last month
· The gunman who killed nine people in a Munich shopping mall - also last month
· The Germanwings pilot who deliberately crashed an airliner in the French Alps in 2015
German doctors who breach patient confidentiality can face up to a year in prison or be forced to pay a fine.
Frank Ulrich Montgomery, the head of the German Medical Association, said: "Patient confidentiality protects patients' privacy and is a basic right under the constitution."
How big is the terror threat?
On deportation, Mr de Maiziere said there would be no tolerance of foreign offenders who used false identities in order to stay in Germany.
The deputy head of Bavaria's intelligence services, Manfred Hauser, has told the BBC the risk of a major attack on German soil is high.
He said his agents were investigating hundreds of reports that the so-called Islamic State (IS) group was sending teams into the country disguised as refugees.
So far Germany has not witnessed the scale of attack seen in France, where militant Islamists killed 147 in Paris last year and 85 in Nice last month.
Mr de Maiziere is expected to attract broad support for creating 4,600 new national security jobs, including 3,250 more police, and for improving police equipment.
Germany is also likely to introduce more video surveillance in urban areas, a special police cyber defence unit and powers to investigate suspects as young as 14.
There will be a big push to intercept terror networks that use the "darknet" to plan attacks or obtain weapons, the minister said. It is an area of cyberspace invisible to ordinary internet users.