The row began last week when a prospective FN candidate for municipal elections next year said on television that she would prefer to see Justice Minister Christiane Taubira "in a tree swinging from the branches rather than in government."
The party immediately dropped the candidate, but Taubira, who is from French Guiana, on Saturday responded with a fierce salvo against the "deadly and murderous thought" of the FN.
"It's blacks in tree branches, Arabs in the sea, homosexuals in the Seine (river), Jews in the oven and so on," she said.
It was not clear what the basis of any FN legal action would be and Taubira said she was unconcerned by the prospect.
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"I'm calmly awaiting the FN's complaint and any court case it leads to," she said today.
The remark that originally sparked the row meanwhile is to be investigated to see if it breaches legislation relating to the incitement of racial discrimination. Judicial sources said the former FN candidate, Anne-Sophie Leclere, would face a preliminary probe that will decide whether there is a basis for prosecution.
"Christiane Taubira is insulted by an FN candidate, and in the end it's the minister who is taken to court by the National Front," Louis-Georges Tin, head of the organisation, said in a statement.
The FN has been seeking a makeover to broaden its voter appeal and dispel its xenophobic image, and appears to be succeeding.
It recently won a key local by-election and is tipped to be the leading French party in European elections also due next year.
In its statement, the CRAN organisation also denounced what it said was a drift to the right of French politics.