Di Maio, whose anti-establishment Five Star Movement (M5S) party governs Italy in coalition with the right-populist League, met with Yellow Vest leader Christophe Chalençon as well as candidates for European Parliament from the anti-government movement on Tuesday.
He added that Italy was a friend and ally of the French people and he was willing to meet the Paris government to resolve differences.
This extraordinary diplomatic rupture between two of the founding members of the European Union and North Atlantic Treaty Organisation allies follows also the accusations launched by Mr Di Maio and his Government partner, interior minister Matteo Salvini, who accused Paris of neocolonialism.
Emmanuel Macron has abruptly canceled his trip to the Munich Security Conference, with the Élysée saying he is focused on domestic issues amidst the ongoing Yellow Vest protests - but German media is seeing Russian Federation in all this.
The big question is whether the spat will have any longer-term repercussions and whether for Italy, it's worth the short-term gain of having got a rise out of France.
Conte, a political unknown who became prime minister a year ago as a compromise between Salvini and Di Maio, was caught on video at last month's World Economic Forum in Davos discussing the dispute with German Chancellor Angela Merkel.
Mr Di Maio has said his populist movement is ready to help France's anti-government protesters, and has accused France of fuelling Europe's migrant crisis.
Italian TV channel La 7 broadcast footage a week ago showing the two leaders talking at a bar, with Conte telling Merkel that Di Maio was attacking France because he was down in the polls ahead of the European elections and needed an enemy.
De Maio's fellow deputy prime minister, Matteo Salvini, has lambasted President Emmanuel Macron directly by saying he is "close, with all my heart.to the French people, the millions of men and women who live in France under a awful government and bad president".
"So they say what are the issues that can help us during the campaign".
France warned him not to interfere in the country's politics.
The two countries have periodically argued about commercial issues including shipbuilder Fincantieri's proposed takeover of France's STX and a past Italian government's contention that landline assets constitute a strategic asset. In 2016, Greece recalled its ambassador to Austria, and in 2017 Hungary withdrew its envoy to the Netherlands.
Paris, anxious about European dependence on Russian energy, said on Thursday -and ahead of a key EU vote- that it wants the bloc's Third Energy Package rules to be applied to the Nord Stream deal.
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