"I am sure you know that Tel Aviv is a wonderful place but be in no doubt that every Jew, and every person, has the right to choose wherever they live", said Rivlin, who also wrote to Macron to thank him for visiting the Jewish cemetery.
This initiative was launched by a number of political parties, including the socialists, President Macron's "Forward, Republic", and the Republicans, who are calling on the French to hold demonstrations throughout the country under the motto "No - to anti-Semitism".
"Enough!" That's the slogan under which French political leaders and thousands of demonstrators rallied across the country yesterday after vandals desecrated almost 100 graves in a Jewish cemetery in eastern France with swastikas.
Macron had received praise from President Reuven Rivlin earlier in the day for his stance on anti-Semitism in France.
However, anti-Semitic violence is believed to be spreading from the old prejudices of the far-right, to radical Islamists and far-left groups, our correspondent adds.
"Government statistics released last week showed there were more than 500 anti-Semitic attacks in the country a year ago, a 74 percent increase from 2017", the wire service reported.
In the past week vandals defaced portraits of the late Holocaust survivor and French minister Simone Veil, scrawled the German word for "Jews" on a Parisian bakery and cut down a tree planted in memory of a Jewish youth tortured to death by an anti-Semitic gang.
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A man walks by graves vandalised with swastikas at the Jewish cemetery in Quatzenheim, France.
Israeli Prime Minister Benjamin Netanyahu expressed his appreciation at France's adoption of the global definition of anti-Semitism, in a phone call with the French leader before the speech, Netanyahu's office said.
"Anti-Zionism is one of the modern forms of anti-Semitism", the French leader said in Paris at the dinner of Jewish umbrella organization CRIF.
During World War II, the French Vichy government collaborated with Germany notably in the deportation of Jews to death camps.
He was set to announce measures to fight the flare-up in anti-Semitism during a dinner with Jewish community leaders later on Wednesday, in an address to the annual dinner of the Representative Council of French Jewish Institutions, Europe's biggest Jewish community. "This incident and that of the attack in Pittsburgh and other anti-Semitic attacks around the world don't stand alone".
A recent Ifop poll of Yellow Vest backers found that almost half those questioned believed in a worldwide "Zionist plot" and other conspiracy theories.