Mohammed Javad Zarif suggested Iran was still willing to talk during an interview with Germany's Der Spiegel magazine.
Whether the troops could receive the Purple Heart for injuries as a result of enemy action is under review.
An early test will be a “million-man” demonstration against the American presence scheduled for Friday.
"I heard they had headaches and a couple of other things … and I can report it is not very serious," Trump said.
The exact number of troops flown to Germany was not immediately clear, but officials said it was a small number.
For days after the Jan. 8 shootdown, Iran denied that it fired missiles at the plane.
Early warning capabilities helped protect U.S. troops on the ground.
Hassan Rezaeifar was quoted by the state-run IRNA news agency as saying "we have no plans to send them out.”
Iran does not have the equipment necessary to be able to analyze the damaged black boxes quickly.
While Iran appeared to be "standing down" from a military response, the cyber threat remains real, said analysts.