The Errand of Mercy Meal Support was a service under the City of San Francisco Sanctuary Program. This service provided the rations which were doled out to Sanctuary District residents at a ration distribution center. (DS9: "Past Tense, Part I")
This service was named on a sign on the ration distribution center in Sanctuary District A. This sign appeared in Star Trek Encyclopedia, 2nd ed., p. 427 and Star Trek Encyclopedia, 3rd ed., p. 427. It did not make an appearance in the 4th edition.
The name of the agency appears to be a reference to the Star Trek: The Original Series episode "Errand of Mercy".