The row broke out after the head of the CRIF Jewish umbrella group said that young Muslims were the cause of all violent crime, prompting a leading Muslim group to boycott the Jewish group's annual dinner, at which Hollande was due to speak.
It rekindled tensions in a country which is home to Europe's largest Jewish and Muslim minorities, just weeks after political leaders called for a spirit of 'national unity' in response to a series of attacks by Islamist militants that left 20 people dead, including three attackers.
"We need to say things clearly: all violence today is committed by young Muslims," Roger Cukierman told Europe 1 radio. "Of course, it's a tiny minority of the Muslim community and Muslims are the first victims."
Cukierman had been asked whether the far-right National Front party bore any responsibility for anti-Semitic acts. Five minors were arrested last week for having damaged hundreds of tombs earlier this month in a Jewish cemetery in eastern France.
Hollande, who did not address the spat directly in his speech at the CRIF dinner, called upon public representatives to measure their words carefully.
In an address focused on discrimination, he said a new law against jihadism would be unveiled in March. He also pressed major Web firms Google and Facebook to agree on how to fight the spread of hate speech online at a conference in April.
"There is no such thing as virtual hatred when it is spreading," he said, referring to racism, anti-Semitism and Holocaust denial. "Major Internet firms must face up to their responsibilities."
Hollande added that criminal courts should handle cases of hate speech rather than those specialising in press freedoms.
Muslim advocacy groups have reported a rise in Islamophobic acts, including vandalism on mosques, after the January attacks at the Charlie Hebdo satirical weekly and a kosher supermarket on the edge of Paris.
The CFCM Muslim umbrella group, in a statement, condemned Cukierman's comments as "irresponsible and unacceptable" and said it would not attend its dinner.
"I don't think Mr. Cukierman is someone who will contribute to us all living together peacefully," Abdallah Zekri, head of a CFCM department that tracks Islamophobic incidents, told BFMTV television.
Cukierman, who did not address his earlier comments, said in his speech that Jews and Muslims were in the same boat and that he hoped the spat would be over quickly.
© Thomson Reuters 2015