France's National Front party founder Jean-Marie Le Pen says he is "ashamed" his daughter - current party leader Marine - still bears his surname.
Amid a growing feud, Mr Le Pen said he hoped she "would get married as quickly as possible so as to change her name".
He added he would not support Marine in presidential elections in 2017.
His remarks came after the far-right party suspended Mr Le Pen, 86, after he repeated his view that the Holocaust was "a detail of history".
Marine Le Pen, 46, has been trying to steer the National Front (FN) away from its racist and anti-Semitic past.
Ms Le Pen's view is that FN's growth is being held back by memories of what it used to be, and that to move to the next level it must cut itself free from its past, the BBC's Hugh Schofield in Paris reports.
Speaking to France's Europe 1 radio, Mr Le Pen said: "I was hoping that the president of the National Front would get married as quickly as possible so as to change her name.
"Because I'm ashamed that she has the same surname as me."
Asked if he would still be supporting his daughter in the presidential elections, Mr Le Pen answered: "Not for the moment."
"[He] seems to have entered a veritable spiral between a scorched earth strategy and political suicide" - Marine Le Pen, 8 April
"Marine Le Pen may want me dead, that's possible, but she must not count on my co-operation" - Jean-Marie Le Pen, 9 April
Mr Le Pen has been suspended but not dismissed by the party - a decision he described as a "felony".
An extraordinary party congress is expected to be held within three months aimed at ending the function of honorary president - which Mr Le Pen has been holding since stepping down as leader in 2011.
Some commentators have suggested he could be more of a risk outside the party than within it.
Mr Le Pen still holds a seat in the European Parliament and a post as a regional councillor in the south of France.
French media on father-daughter feud
Dominique Albertini in Liberation notes that Marine Le Pen "dealt with the paternal problem in the most radical way".
Le Parisien goes further, saying that the move was the "denouement of an unprecedented political and family crisis" and describes her decision as "Oedipal".
But some regional papers say that Mr Le Pen could still be dangerous.
Patrice Chabanet in the Journal de la Haute-Marne warns Marine to guard against her father who "is not a man to be dictated to" and warns of his "capacity to do harm".
Laurent Bodin in L'Alsace agrees, saying that even outside the party, her father is a "thorn" in its side.
Jean-Marie Le Pen: A career in controversy
- 1987 - First makes his infamous remarks describing the Holocaust as a "detail of history"
- 1997 - Assaults rival Annette Peulvast-Bergeal during parliamentary election campaign
- 2006 - One of many convictions for inciting racial hatred over inflammatory remarks about France's Muslim population
- 2007 - Tells Le Monde newspaper "you can't dispute the inequality of the races"
- 2015 - Repeats views on the Holocaust, prompting Marine Le Pen to accuse him of trying to "rescue himself from obscurity"