"We will not give the right wing free rein to do whatever it wants," he said in northern Mexico.
"We are going to fight them."
Lopez Obrador has timed the launch of his opposition government to coincide with the anniversary of the 1910 Mexican revolution when Francisco Madero, Emiliano Zapata and Pancho Villa took up arms against conservatives to found modern Mexico.
The former mayor of Mexico City has encouraged supporters to donate to his alternative administration on his website.
Since Calderon was announced the winner, Obrador and his supporters have carried out a number of demonstrations to protest the decision.
"Those neofascist reactionaries better not think they'll have room to maneuver. We're going to keep them on a short leash," he said on Saturday.
In particular, he said he would monitor any move by the Calderon administration to privatise the state-run oil industry.
"We'll gather thousands, millions of people to prevent that from happening," he said.
Lopez Obrador's party also has vowed to boycott Calderon's swearing-in ceremony, insisting that the July election was won by fraud and that the president-elect "is undeserving of any respect or consideration."