The demand comes after he reportedly said that the fascist dictator Benito Mussolini "built roads" in Italy and achieved other "positive things" before following Adolf Hitler into war.
The dictator had ruled Italy from 1922 to 1943 and was a key ally of Hitler's Nazi regime.
Tajani’s remarks prompted outrage and, demanding his resignation, the GUE/NGL group expressed its “shock and outrage” at the statements made on Italian radio.
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The group said it was “a clear attempt to normalise fascism”.
Tajani, an Italian EPP MEP, reportedly said that “before the war, Mussolini did positive things. Until the war and the alliance with Hitler, until the race laws, apart from the dramatic assassination of Giacomo Matteotti, Mussolini did good things like infrastructure. You have to be honest.”
In response, GUE said, “The fascist regime in Italy was a tragedy that spread worldwide, culminating in a world war that killed hundreds of millions with unprecedented destruction. Mussolini annihilated the Italian parliament at the start of his regime, and his orders to kill or jail political opponents included Socialist leader Matteotti, murdered in 1924, and Antonio Gramsci who was jailed in 1927.”
“Tajani’s statements are outrageous and completely unacceptable. How can someone who represents the main democratic institution in the EU resort to the same old slogans that fascists and the extreme right have being using since the end of the war to justify the Mussolini regime.”
“Tajani’s statements are outrageous and completely unacceptable … This Parliament cannot be represented by a President who tolerates the fascist initiator himself” GUE/NGL group statement
The statement said the group “demands Tajani’s immediate resignation,” adding, “Europe is now facing a tough fight against the extreme right and openly neo-fascist organisations. This Parliament cannot be represented by a President who tolerates the fascist initiator himself.”
Later on Thursday, Tajani hit back, saying, “As a convinced anti-fascist, I apologise to all those who may have been offended by what I said, which in no way intends to justify or play down an anti-democratic and totalitarian regime.”
“I am deeply saddened that, despite my personal and political history, some may feel that I would choose to be lenient with regards to fascism.”
“I have always been whole-heartedly anti-fascist. I have always stressed that Mussolini and fascism were the darkest chapter in the history of the past century, without any distinction. I have always fought against any form of dictatorship or totalitarianism,” Tajani added.
This is the second time this year that Tajani has prompted outrage with historically-charged statements. Last month, he angered Slovenia and Croatia by referring to parts of the countries' territories as "Italian."
In the past, Italy controlled regions of Istria and Dalmatia, but the Adriatic areas went to Yugoslavia after World War II and later passed to its successor states.
“I apologise to all those who may have been offended by what I said, which in no way intends to justify or play down an anti-democratic and totalitarian regime” Antonio Tajani
At a memorial event for alleged victims of the Yugoslav army in February, Tajani ended a speech with "Long live Italian Istria, long live Italian Dalmatia."
Slovenia later accused Tajani and Italy’s Interior Minister Matteo Salvini of historical revisionism.
A mere week later Tajani found himself once again facing the music for reportedly accepting an invitation to attend the World Congress of Families conference in Italy.
Campaigners and MEPs say the event is organised by the International Organisation for the Family (IOF), saying this is an “umbrella organisation known for its anti-LGBTI agenda.”