A French newspaper added to the pressure on the outspoken Dieudonne, reporting that he owes tax authorities more than €800,000 and is being investigated for suspected money laundering.
Weighing into a debate that has gripped France, Hollande urged local officials to apply an interior ministry circular authorising city mayors or police chiefs to cancel performances of the comic, Dieudonne M'Bala M'Bala, on public order grounds.
Several cities and towns, among them Nantes and Bordeaux, have declared prohibitions on shows of the comedian, who goes by his first name. Officials said there was a risk of violent clashes between fans and protesters.
Police in Paris are also "seriously considering" banning an upcoming show in the capital, an informed source said.
Hollande said the interior ministry instructions were to "ensure that no one can use a performance for the goals of provocation and the promotion of overtly anti-Semitic theories," without specifically mentioning Dieudonne.
But the bans are expected to face legal challenges on freedom of speech grounds.
Dieudonne's lawyer Jacques Verdier said his client would "act immediately" against any performance ban.
Dieudonne's tour was to have started on Thursday in Nantes and run until June. He appears to be guaranteed an audience in Switzerland at least, where he is due to play for 10 nights in a 460-seat venue in the small town of Nyon.
Local official Olivier Mayor told AFP that Dieudonne could not be banned there because of a precedent set when Geneva tried to ban him several years ago with a decision that was overturned by a judge.
"You can't convict someone in advance, we live by the rule of law," Mayor said.
Attempts to ban Dieudonne have also sparked misgivings amongst some opponents of the comic in France, who fear that such moves only fuel his popularity with his target audience and enhance his opportunities to cash in on the notoriety.
Dieudonne, 47, is the son of a father from Cameroon and a white French mother. He has been performing anti-Semitic material for years but gained greater prominence in recent months as a result of the Internet-driven success of the "quenelle", his trademark straight arm gesture which some have described as a reverse Nazi salute.
Footballer Nicolas Anelka, a former member of France's national team, stirred up a row by performing the gesture during a goal celebration for his English club West Brom last month.
Defenders of the comic say the gesture is simply a coded "up yours" directed at the French establishment and thousands of ordinary French people have used it without being aware of any racist overtones.
The gesture has taken on sinister connotations, however, with the publication of pictures of Dieudonne fans performing quenelles outside synagogues, at a holocaust museum and in front of the school in Toulouse where in 2012 an Islamist gunman killed a rabbi and three Jewish children.
Dieudonne's popularity - more than 5,000 tickets have been sold for the opening night of his tour - has exacerbated concern over a perceived resurgence of anti-Semitism in France under the guise of a brand of anti-Zionism.
Coming in the wake of a series of incidents last year in which the country's most prominent black politician, justice minister Christiane Taubira, was subjected to monkey taunts, concerns have risen that overt racism is becoming dangerously acceptable in France.
The trend has been linked by some to the rising electoral popularity of the anti-immigration, anti-EU National Front (FN), founded by Jean-Marie Le Pen, who is the godfather to one of Dieudonne's children.
Le Pen's daughter, Marine, who succeeded him as party leader, says she is as shocked as anyone else by the comic's anti-Semitism, but believes the government is wrong to try and ban him.
She added that she believed there was a sort of "personal vendetta" against him by interior minister Manuel Valls.
Le Monde daily has reported that public prosecutors in the city of Chartres, southwest of Paris, launched the money laundering probe in February last year over suspicions the comedian was illegally sending money to Cameroon.
The paper said the comic "owes tax authorities €887,135 ($1.2 million)," but did not give a source.
The French finance ministry's anti-money laundering department Tracfin would not confirm or deny the report.