“The infection numbers are still far too high — much higher even than a fortnight ago,” Altmaier told the Bild an Sonntag newspaper ahead of a government meeting on Monday to assess the progress of the restrictions.
Germany went into partial lockdown in early November, closing bars, restaurants, gyms and other recreational facilities but keeping schools and shops open.
The number of new infections per day has since slowed but remains high, with a record of more than 23,000 reported on Friday.
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“We will have to live with considerable precautions and restrictions for at least the next four to five months,” Altmaier said.
“Many people are now understandably hoping for a loosening (of restrictions), that restaurants or cinemas will reopen. But in view of the still far too high infection rates, we have little room for manoeuvre.”
The restrictions agreed by Chancellor Angela Merkel and the leaders of Germany's 16 states are provisionally in place until the end of November.
But the leaders will meet again on Monday to decide whether to extend them or to introduce sharper restrictions.
READ MORE: Is Germany set to tighten shutdown measures?
With more than 300,000 schoolchildren in quarantine, calls have been growing for schools to shut or at least move more of their lessons online.
“We are entering a situation where school operation is becoming a high risk for children, teachers, parents and grandparents,” MP and epidemiologist Karl Lauterbach said in an interview with the Funke media group.
Several demonstrations against the restrictions were held on Saturday across Germany, including one in Frankfurt where water cannons were used against counter-demonstrators.
A protester reacts as police use water cannons to disperse a demonstration against coronavirus restrictions on November 14, 2020, in Frankfurt am Main, western Germany. Yann Schreiber / AFP
Germany has registered a total of 790,503 coronavirus cases and 12,485 deaths, according to the Robert Koch Institute disease control centre.
The number of Covid-19 patients in intensive care has soared from just over 360 in early October to more than 3,300 currently.
Neighbouring Austria, which also imposed a partial lockdown two weeks ago, announced on Saturday that schools and non-essential shops will close from Tuesday.