"We are filing this contest to make absolutely sure every valid vote was counted and no one's was counted more than anyone else's," Coleman said.
Coleman shrugged off the idea that he might concede the election to avoid a protracted fight that could leave Minnesota with only a single senator in Washington for months.
"Something greater than expediency is at stake here," Coleman said. He added: "Democracy is not a machine. Sometimes it's messy and inconvenient, and reaching the best conclusion is never quick because speed is not the first objective, fairness is."
State law prevents officials from issuing an election certificate until legal matters are resolved.
Franken attorney Marc Elias called Coleman's lawsuit "essentially the same thin gruel, warmed-over leftovers from meals we've all been served over the last few weeks."
He said that Coleman has the right to sue, but that doesn't mean his claims have merit, and he is confident Franken would prevail.
Franken e-mailed supporters Tuesday to request donations to continue the fight, just as Coleman did a day earlier.
Coleman, whose term expired Saturday, led Franken by 215 votes in the Nov. 4 count but that advantage flipped during a prolonged recount.
In going to court, Coleman has three big challenges: raising money to pay escalating legal bills, proving the election was flawed and managing the public's desire to have the race over.
"They definitely have an uphill fight on their hands," said Guy-Uriel Charles, a professor of election and constitutional law at the University of Minnesota. "Their legal theory will have to overcome a burden of proof, and then they have to find enough votes to overcome Franken's lead."
That could prove difficult, since any bloc of new votes would almost surely include some for Franken, who declared victory Monday.
A lawsuit gives both sides options they lacked during the recount, such as accessing voter rolls, inspecting machines and introducing testimony from election workers.
Coleman's filing includes some of the points his lawyers have been making for weeks. It centers mainly on claims that hundreds of rejected absentee ballots from Republican-leaning areas should have been part of the recount, that some ballots in Democratic territory were counted twice and that election officials were wrong to use machine tallies for a Minneapolis precinct where ballots went missing.
But there are new angles, too.
The lawsuit alleges that the Canvassing Board made mistakes when determining voter intent on challenged ballots, that ineligible voters cast ballots and that some absentee ballots were erroneously opened early, raising chain-of-custody concerns.
A race that was a couple of years in the making - Franken announced his campaign in February 2007 - is now two months past Election Day.
The case would fall to a three-judge panel selected by Chief Justice Eric Magnuson of the state Supreme Court, an appointee of Republican Gov. Tim Pawlenty and a member of the Canvassing Board.
The costs of the election lawsuit fall to the losing campaign, although state law could require various units of government to foot the bill if their errors or irregularities lead to a reversal.