Democratic lawmakers and even some Trump administration officials believe he is too untrustworthy to benefit from the historical practice accorded to former presidents.
Minister of Defence Trine Bramsen says an investigation will look into the matter "with the utmost seriousness".
The three soldiers were stationed at a specialised parachute training centre under the authority of the country's external intelligence agency, the DGSE
"I can honestly say that it pains me. Everyday I try to build a better relationship with Russia and on the other hand, there is such hard evidence that Russian forces are doing this," the German chancellor told lawmakers.