INDIANAPOLIS — The grandson of the late U.S. Rep. Julia Carson won a special election Tuesday to succeed her, keeping the seat in Democratic hands and becoming the second Muslim ever elected to Congress.

Democrat Andre Carson had a 5,000-vote lead over Republican Jon Elrod out of nearly 59,000 votes counted. With 88 percent of 445 precincts reporting, Carson had about 53 percent of the vote compared with about 44 percent for Elrod.

Carson will represent a district that covers most of Indianapolis for the remainder of the year. In a primary in May, he’ll seek to be the Democratic nominee for a full two-year term.

In his victory speech, Carson told more than 100 supporters gathered at a downtown Indianapolis hotel that he would have to “hit the ground running.” One of his top priorities, he said, would be ending the war in Iraq.

“We need to bring our men and women back home and end this useless war,” Carson said.

Elrod held out hope for a late surge and did not concede defeat. Elrod campaign manager Kyle Casting said the candidate would not give up until the last vote was counted.

“We are waiting for the last ballots to come in. There are several precincts left to come in,” Casting said.

Mississippi was also choosing candidates Tuesday to fill two rare open congressional seats. One of those seats became vacant when Republican Roger Wicker was appointed to replace Sen. Trent Lott after his resignation.

In Indiana, District 7 is predominantly Democratic and Carson had a large fundraising advantage over Elrod, along with more than $150,000 in spending by the Democratic Congressional Campaign Committee on Carson’s behalf.

But Carson also faced several obstacles including expected low voter turnout and potential backlash over complaints of political nepotism.

Elrod had promoted himself as a moderate focused on fiscal reforms, such as eliminating most earmark funding for projects sought by members of Congress. He had also refused to join the other 48 Indiana House Republicans in backing a state constitutional amendment to ban gay marriages.

Both candidates are young and have little political experience.

Carson, 33, has been a member of Indianapolis City-County Council since August. Elrod, 30, is a first-term state representative who won election in 2006 by eight votes over a five-term Democratic incumbent.

Also on the ballot is Libertarian Sean Shepard. Shepard had about 3 percent of the vote.

Julia Carson, a Democrat who first won election to Congress in 1996 and died in December, was the first black to represent Indianapolis in Congress — from a district that is nearly two-thirds white.

Carson, whose grandmother raised him in a Baptist church, converted to Islam more than a decade ago.

Carson will join Rep. Keith Ellison, D-Minn., as the only Muslims in Congress. His religious identity has drawn little attention during the campaign, and Carson said he doesn’t believe it hurts him politically.

“I’m a proud Hoosier,” Carson said after his speech Tuesday night. “I’m an Indy 500 Hoosier, I’m a Covered Bridge Festival Hoosier, I’m a Black Expo Hoosier, I’m a state fair Hoosier. I just happen to be a Hoosier of the Muslim faith.”

In Mississippi, Republicans and Democrats were choosing their candidates for two congressional seats.

Mississippi’s 3rd District is open for the first time in 12 years after Republican Rep. Chip Pickering decided not to seek a seventh term. The heavily Republican district stretches from Oktibbeha County in the north to Adams and Wilkinson counties in the southwest.

Former state Sen. Charlie Ross and attorney Gregg Harper are heading for a runoff in the Republican primary. The winner will face Democrat Joel Gill.

Democrats say they have a chance to claim north Mississippi’s 1st District. The district leans Republican but could be a toss-up this fall. Prentiss County Chancery Clerk Travis Childers and state Rep. Steve Holland were headed for a runoff in the Democratic primary. On the GOP side, former Tennessee Valley Authority chairman Glenn McCullough and Southaven Mayor Greg Davis also were headed to a runoff.

A runoff in the congressional races will be April 1. The general election is Nov. 4.