The image represents Greater Hungary – the old Hungarian imperial territory that existed before Austria-Hungary’s defeat in World War One.
Romania voiced “firm disapproval” of Mr Orban’s gesture, in a message to the Hungarian ambassador to Bucharest.
Ukraine demanded an official apology.
Ukraine’s foreign ministry spokesman Oleg Nikolenko said Kyiv was summoning Hungary’s ambassador “who will be informed of the unacceptability of Viktor Orban’s act”.
“The promotion of revisionist ideas in Hungary does not contribute to the development of Ukrainian-Hungarian relations and does not correspond to the principles of European politics,” he said on Facebook.
Mr Orban’s Facebook page has a video showing him greeting Hungarian footballers and sporting the scarf, which he wore during a match between Hungary and Greece on Sunday.
About 1.2 million ethnic Hungarians live in Romania and 150,000 in western Ukraine. There have been tensions previously over Mr Orban’s efforts to promote Hungarian identity in both countries.
In its protest on Monday the Romanian foreign ministry said “any revisionist manifestation, regardless of the form it takes, is unacceptable, contrary to the current realities and commitments undertaken jointly by Romania and Hungary”.
The old Hungarian territory also included parts of what are now Austria, Croatia, Serbia and Slovakia.
On Facebook Mr Orban said the Hungarian national team was “the team of all Hungarians wherever they live”.
“Football is not politics. Let’s not see what is not there,” he said.
For years Mr Orban has been widely criticised in Europe for curbing media freedom and the rights of minorities and civil society groups, as well as for his longstanding friendship with Russian President Vladimir Putin.
He has been accused of undermining the EU’s core values, while he accuses Brussels of overreaching its powers.
Source : BBC