Interior Minister Thomas de Maiziere also announced plans to speed up the deportation of foreign criminals.
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.