The unofficial tally, which will probably be certified Thursday, showed Alexander with 86,718 votes and Fletcher with 85,744 -- a margin of 974 votes.
The tally immediately after Saturday's election showed Alexander winning by 518 votes, 85,720 to 85,202.
Alexander picked up votes after parish officials double-checked the voting machines. In Allen Parish, for example, a machine failed to print out the numbers Saturday, and court officials had to read the impressions on the paper. On Tuesday, they were able to get an accurate reading.
Fletcher, who had said he wanted to see the certified results before deciding whether he will challenge the outcome, conceded Tuesday and congratulated his opponent.
"I extend an offer to assist Mr. Alexander in any manner I can which helps our district," Fletcher said. "It is time to pull together and work for the people with dignity, not divisiveness" -- a reference to the hostile exchanges that marked the entire campaign.
Alexander was in Washington on Tuesday, looking for a place to live, according to spokesman Wooten Johnson. Alexander will be sworn in Jan. 7.
Alexander succeeds John Cooksey, a Republican who left Congress after three terms to make a failed bid for the U.S. Senate. Fletcher is the congressman's former chief of staff.
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