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Tria was due to meet French Finance Minister Bruno Le Maire in Paris later on Wednesday, one of Tria's first important encounters since he took office in Italy's new anti-establishment government.
Tria is still due to meet German Finance Minister Olaf Scholz on Thursday in Berlin, the source said.
Earlier on Wednesday, Italy's foreign ministry summoned the French ambassador over remarks made by French President Emmanuel Macron condemning Rome's decision to close its ports to humanitarian rescue ships.