(CNN) - Democrat Paul Carmouche Wednesday conceded his race for a seat in Congress to physician John Fleming in Louisiana's 4th congressional district.
Louisianans went to the polls Saturday to choose between Carmouche, the former Caddo Parrish district attorney, and Fleming. Unofficial results show Fleming leading Carmouche by less than 400 votes.
"Of more than 92,000 votes cast throughout the 13 parishes of this district, it appears that our campaign has fallen slightly short," Carmouche said. "I will not ask for a recount of any of the paper ballots, and I offer my warmest congratulations to Dr. Fleming."
Fleming takes the seat held by long-time Republican Rep. Jim McCrery, who is retiring after 10 terms in office.
Elections in the 4th district and the 2nd district - won by Republican Anh "Joseph" Cao over indicted Democratic incumbent Rep. William Jefferson - were delayed because of Hurricane Gustav in August.
In those two districts, the Democratic and Republican primaries were held on November 4.
Fleming's election gives the GOP 178 seats in the House of Representatives. The Democrats hold 256, and there is one seat still unresolved - the 5th congressional district of Virginia.
In that race, Democratic challenger Tom Perriello was certified the winner over incumbent Republican Rep. Virgil Goode, but the margin - less than 800 votes - was close enough for Goode to request a recount under state law.
The recount takes place on Tuesday.