"We will never accept any form of collaboration or alliance, either in ideas or at the ballot box, between the far-right and the right that calls itself Republican," he said, alleging that the governing UMP party has appropriated the policies of the Front National.
"We must stop this drift that turns Claude Guéant from a high-ranking state official into a sad copy of Bruno Gollnisch," he said during his closing speech at the party conference this weekend.
The 61-year-old Gollnisch has been a prominent member of the Front National since winning the seat he still holds today in the European parliament in 1989. He also served as a member of the French parliament from 1986 until 1988 and has held a variety of senior roles in the party.
He stood for the leadership of the party in January 2011 against the eventual victor and current leader, Marine Le Pen.
Désir's hard-hitting offensive, which also criticized a "rancid right" that "compares homosexuals to animals and requires DNA tests for immigrants" prompted an equally fierce counter-attack.
Government spokesperson and budget minister Valérie Pécresse was first on the airwaves on Sunday evening, accusing Désir of "unacceptable mistakes." She demanded that his fellow Socialists condemn the remarks.
Guéant's predecessor at the interior ministry, Brice Hortefeux, told radio station Europe 1 on Monday that he had been "sincerely shocked" that none of the Socialist candidates for the presidential nomination had slammed the comments.
Rather than condemn the interim leader, Socialist spokesman Benoît Hamon was happy to back Désir's comments at a press conference on Monday, saying they were "well expressed."
"It's Marine Le Pen who proposed an honorary membership of the party to Mr Guéant because he had adopted her policies," he said. "If Mrs Le Pen thinks Mr Guéant lives up to the Front National programme, then it's not surprising one would draw these conclusions."