Democrats celebrated a victory on Saturday in Gabrielle Giffords's former Congressional district in Arizona, while a recount of early-voting ballots began in a closely watched House race in Florida.
The races were in two of the few remaining districts where winners were still undecided after the Nov. 6 election. Democrats were hoping to win both races to help close the gap between their party and the Republican majority in the House of Representatives.
The former district director for Ms. Giffords, Ron Barber, had enough votes on Saturday to win the race for Arizona's Second Congressional District. Mr. Barber won a special election to fill Ms. Giffords's seat in June. But on Nov. 6, he barely eked out a victory over the Republican candidate, Martha McSally, a retired Air Force colonel, in an election for a full two-year term.
By Saturday, it became clear that Ms. McSally could not overtake Mr. Barber's 1,402-vote lead in the district, which includes parts of Tucson and southeastern Arizona. Mr. Barber said Ms. McSally called him on Saturday to concede the race.
In a statement, Mr. Barber thanked his supporters and said he was eager to get back to Washington.
"Our charge is clear: to stand up for middle-class families and look out for Southern Arizona's future," Mr. Barber said.
The victory gave Democrats a sweep of all three competitive House races in Arizona.
In Florida's 18th Congressional District, a recount of early-voting ballots began on Saturday. The St. Lucie County Canvassing Board voted 2 to 1 late Friday to order the recount after Representative Allen B. West, a Republican, complained about a series of tabulation errors.
Earlier Friday, Judge Dan L. Vaughn of St. Lucie County Circuit Court had agreed with arguments made by lawyers for Patrick Murphy, Mr. West's Democratic opponent, and lawyers representing county election officials and the canvassing board that the court had no authority to order a recount. But the judge said that Mr. West's campaign could contest the election if it was not satisfied with the results.
Mr. West, who was elected to the South Florida seat two years ago with support from the Tea Party, had called for a recount in Palm Beach County after it appeared he was losing to Mr. Murphy. Although Mr. West refused to concede, Mr. Murphy went to Washington last week and, at a news conference held by Democrats, called for bipartisan cooperation.
On Saturday, Mr. Murphy's campaign filed an injunction to stop the recount, but later in the day Judge Larry Schack of St. Lucie Circuit Court denied the emergency motion. Judge Schack said that if either candidate was unhappy with the ultimate vote count, the law gives them the option of formally contesting the election once it is certified this week, The Associated Press reported.
On Friday night, Mr. West's campaign said it was pleased with the decision to recount the ballots.
"This is what we have requested all along, and it will move us toward a fair and accurate result," the campaign said in a statement. "It's unfortunate that Patrick Murphy and his lawyers tried to prevent this recount from occurring."
St. Lucie County election officials have until Sunday to certify the election results, and the state's deadline is Tuesday.
Democrats held on to the Senate in the election, while Republicans kept the House, guaranteeing at least two more years of divided government. Modest gains made by Democrats in the House prevented bigger losses.
For Mr. Barber, it has been a long journey to a full term in Congress. He was with Ms. Giffords at a Tucson shopping center in 2011 when a gunman opened fire, killing six people. Mr. Barber was shot in his groin and cheek, and he spent months in physical therapy. When Ms. Giffords stepped down from Congress, Mr. Barber decided to run for her seat.
This month, the gunman, Jared L. Loughner, was sentenced to seven consecutive terms of life in prison for the shooting.
This article originally appeared in The New York Times.