Socialists candidate Rumen Radev won Sunday's presidential election by a wide margin.
The former opposition leader has pledged to act as a neutral "refugee" in the country's heated political scene.
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The coordinated trip comes as rebels advanced on a railway hub held by Ukrainian troops.
Berlusconi's petition to have the sentence reduced was filed last month and approved on Monday.
The Greek government began negotiations with the head of the eurozone finance ministers in Athens.