The court said it needed until Monday to reach a conclusion and cancelled a session scheduled for Friday.
Boere is charged with killing three men: Frans Kusters, a member of the Dutch resistance; Fritz Bicknese, a chemist; and Teun de Groot, a bicycle seller who helped hide Jews fleeing Nazi persecution.
Heinrich Boere managed to avoid prosecution for the Dutch killings until recently
He was captured by US forces in The Netherlands after the war.
Boere confessed to killing the three civilians in 1944 while a member of an SS death squad which hunted anti-Nazi resistance fighters.
He escaped and fled to Germany before being sentenced to death in absentia in the Netherlands in 1949, a sentence that was later reduced to life in prison.
After refusing a 1980 Dutch extradition request, a German court indicted him in 2008.
In January, the case nearly collapsed after a court said Boere, who is of Dutch-German origin, was unfit for trial, due mainly to a heart condition.
The ruling was overturned by an appeal court.
Georg Winkel, a spokesman for the court in the western city of Aachen, said Boere would undergo a medical examination every day of the court proceedings.
Winkel said he did not know if Boere, who on the Simon Wiesenthal Centre's list of top ten second world war criminals, would plead guilty to the murder charges.