Berlin last year also announced stricter controls on its land borders with Poland, the Czech Republic and Switzerland.
Those, and controls on the border with Austria, had allowed it to return 30,000 migrants since October 2023, it said on Monday.
Ms Faeser said a new model would enable the government to turn back many more – but it could not talk about the model before confidential negotiations with the conservatives.
The controls could test European unity if they lead to German authorities requesting other countries to take back substantial numbers of asylum seekers and migrants.
Under EU rules, countries in the Schengen area, which encompasses all of the bloc bar Cyprus and Ireland, are only allowed to introduce border checks as a last resort to avert threats to internal security or public policy.
Germany shares its more than 3,700-km-long (2,300 miles) land border with Denmark, the Netherlands, Belgium, Luxembourg, France, Switzerland, Austria, the Czech Republic and Poland.
Austria’s Interior Minister Gerhard Karner told Bild newspaper on Monday that his country would not take in any migrants turned away by Germany at the border.
“There’s no room for manoeuvre there,” he said.
The measures may not immediately result in many more migrants being turned away at the border, but they could result in more returns to other European countries down the line, as well as acting as a deterrent, said Susan Fratzke at the Migration Policy Institute.
The number of asylum applications in Germany already fell 21.7pc in the first eight months of the year, according to government statistics.