A 29-year-old Southeast Washington man who already faces rape and murder charges in Montgomery County has been charged in the District with murder in the strangulation of a 66-year-old housekeeper two months ago in an affluent section of Northwest Washington.

Mitchell M. Moore was charged Friday in the death of Teresa Nelson, whose body was found in the dining room of the house where she worked at 2829 Woodland Dr. Police said at the time that Nelson had been "viciously and brutally beaten."

Nelson was killed on Oct. 10. Two days later, Marie Workman, 23, was stabbed and strangled while taking care of three children in her apartment on Columbia Pike in Silver Spring. Three days after that, on Oct. 15, a 35-year-old woman in the Foxhall area of Northwest Washington was beaten by a man who had knocked on her door and asked directions, police said.

Moore, whose address was listed as 2711 Robinson Place SE, was arrested the day of the Foxhall area incident, and charged with burglary in connection with it, according to the U.S. attorney's office. The next day, Montgomery County police said they had obtained arrest warrants charging Moore with murder in the death of Marie Workman. They said they had also charged him in a warrant with the rape of another woman in September.

In an affidavit filed in support of an arrest warrant in the death of the housekeeper, D.C. police said they had found a link between that killing and the Foxhall burglary.

In the burglary, police said, a man allegedly entered a house in the 4400 block of Edmunds Street NW "by inquiring for directions and showing pictures of individuals he was attempting to locate."

"He seemed so genuine," the burglary victim said in describing the intruder to a reporter.

After reports appeared in the media, police said in the affidavit, a witness told them that on the day the housekeeper was killed someone had come to the witness' door and "made similar inquiries."

Police said the witness later followed the man to within three blocks of the Woodland Drive address where the housekeeper was killed. The witness later attended a lineup at police headquarters and identified someone there "as the subject he had encountered on October 10 . . . , " according to the affidavit.

Moore, who was held under preventive detention after his arrest in the Edmunds Street incident, was placed under arrest on Friday in the death of Nelson, according to Assistant U.S. Attorney Thomas P. Murphy. He pleaded not guilty in Superior Court the same day and was ordered held without bail pending a preliminary hearing, Murphy said.