"It may be tempting for some to dismiss this as a complaint from a sore loser," Hendrix said at a news conference. "But there has been enough evidence ... to raise legitimate questions about how the election was conducted and how the ballots were counted."
Arthur Blackwell II, the mayor's chief campaign strategist, said that with more than 14,500 votes separating the candidates, a recount likely won't change the outcome.
"This is sour grapes," Blackwell said. "This is not really in the city's best interests.
Hendrix announced his decision the same day the city's Board of Canvassers certified the Nov. 8 vote. Kilpatrick received 123,140 votes, or 53 percent, to 108,600 votes, or 47 percent, for Hendrix.
Unofficial totals earlier had Kilpatrick with 123,067 votes, or 53 percent, to Hendrix's 108,539 votes, or 47 percent.
The request comes as Detroit is facing a budget deficit that's estimated to grow to as much as $300 million by next year. Kilpatrick spokesman Howard Hughey said the recount could cost the city nearly $600,000.
The secretary of state's office had been working with the city to prepare for the final vote certification and to identify any problems with the count.
Following the vote, officials reported that at 17 of the city's 720 precincts test votes weren't cleared from tabulating machines before actual votes were cast, leading to some changes in the totals.
And eight precincts weren't included in the initial vote count because information wasn't properly delivered to the Detroit city clerk's office, state elections officials have said.
On Election Day, the Justice Department obtained an order for the secretary of state to preserve absentee ballots and related materials from the mayor's race.
The department said it was investigating allegations that votes were cast using the names of dead people and that the city clerk improperly helped incapacitated people vote by absentee ballot.