Janos Boka, the EU affairs minister of Hungary, unveiled the provocative slogan at a press conference in Brussels.
“I’m not sure if President Trump ever wanted to make Europe great again,” he said when asked about the choice of motto.
“This is a reference to an active presidency,” he claimed.
Mr Orban has repeatedly backed Mr Trump to win the US presidential elections in November and claimed he will end the war in Ukraine.
“We can’t get involved in another country’s elections, but we would really like President Donald Trump to return to the presidency and make peace here in the eastern half of Europe,” he said in February.
“Make Europe great again!” he added. “MAGA there, MEGA here.”
Hungary has said it will focus on defence, energy cooperation, migration and the enlargement of the EU to countries in the Western Balkans during its presidency.
There are fears in Brussels that Budapest will try to use the presidency for its own ends, rather than act as an honest broker to find consensus, as it is meant to do.
The incoming presidency, which will see Hungarian diplomats chair important meetings, also unveiled the Rubik’s cube as its logo.
The puzzle was invented by a Hungarian and was described as “the essence of Hungarian genius” by Budapest’s Europe minister.