It promises to reopen many of the disputes that arose during the recount, and to raise new questions about the conduct of the election and the counting of ballots.
Coleman acknowledged a desire among some Minnesotans to move on, but said a larger principle than expediency is at stake.
"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," he said at a Capitol news conference filled with cheering supporters.
"Democracy is not a machine," Coleman said. "Sometimes it's messy and inconvenient, and reaching the best conclusion is never quick because speed is not the first objective, fairness is."
Republican Gov. Tim Pawlenty, who will eventually sign the winner's election certificate, backed Coleman's position Wednesday.
"It's disappointing that it's going to take longer but I think the more important thing to focus on is, the court process will allow ... everybody to say every stone was turned over, and in the end then have more confidence in the result," Pawlenty said.
A state board on Monday determined that Franken captured 225 more votes in the November election. But Minnesota law prevents officials from issuing an election certificate until legal matters are resolved. Franken did not participate Tuesday when new U.S. senators took the oath of office in Washington.
A trial is supposed to commence within three weeks of the case being filed.
Coleman attorney Fritz Knaak estimated the lawsuit could take at least two months to resolve.
Franken attorney Marc Elias called the lawsuit "essentially the same thin gruel, warmed-over leftovers from meals we've all been served over the last few weeks."
