An online petition which calls for the "immediate resignation" of the Italian centre-right deputy has attracted more than 3,000 signatories.
Tajani is said to have caused “great offence” in a speech he made at a ceremony commemorating Italian victims of World War II massacres.
The deputy had spoken, along with Italy’s interior minister Matteo Salvini, in Basovizza, near the Slovenian border.
The spot is close to where many of the victims were killed by Tito’s Yugoslav partisans and often thrown alive into deep sinkholes known as “foibe”.
Slovenian president Borut Pahor reacted to the speech by saying he was “deeply concerned by inadmissible statements by senior Italian officials suggesting that the foibe (killings) represented ethnic cleansing.”
Further condemnation came from Slovenian Prime Minister Marjan Sarec, who said, “It’s unprecedented historical revisionism. Fascism was a fact and its objective was destroying the Slovenian people.”
Tajani responded immediately to the criticism by issuing a statement in which he apologised for causing any offence, adding that it was “not my intention to offend anyone.”
“If President Tajani wants to be a nationalist politician rather than a statesman he should leave his role as President of the European Parliament" Udo Bullman MEP
"I'm sorry if the meaning of my words has been misinterpreted," Tajani said during the parliament's plenary session in Strasbourg earlier this week.
"It was not my intention to offend anyone. I just wanted to send a message of peace between the peoples, so that what happened then will never be repeated," he added.
Tajani further reacted on his personal twitter account, saying, "History is history".
In his earlier statement, he said, “In my speech, I wanted to highlight the path to peace and reconciliation between the Italian, Croatian and Slovenian peoples and their contribution to the European project.”
“My reference to Istria and Italian Dalmatia was in no way a territorial claim. I was referring to the Istrian and Dalmatian Italian-language exiles, their children and grandchildren, many of whom were present at the ceremony.”
However, his apology appears to have done nothing to defuse the situation, with some MEPs now joining a call for him to stand down as Parliament’s President.
The petition, seen by this website, says his words were "unacceptable" and the signatories allege that Tajani's comments were "undoubtedly expressing fascist, irredentist tendencies", which are "absolutely inappropriate" in the 21st century.
Those reportedly calling for his resignation include Jadranka Kosor, former prime minister of Croatia, Milan Kucan and Danilo Turk, former presidents of Slovenia, and Stjepan Mesic, former president of Croatia.
According to media reports, among several MEPs said to be backing the petition are Croatian Socialist deputy Biljana Borzan; Slovenian Greens member Igor Šoltes and Austrian Socialist MEP Josef Weidenholzer.
Earlier this week, ECR leader Syed Kamall wrote to Tajani, asking him to retract the offending part of his speech.
The letter from the UK Tory deputy, dated 13 February and seen by The Parliament Magazine, said, “I am writing to you on behalf of the ECR Group in response to the speech you gave over the weekend in Basovizza, Italy.”
“Unfortunately, as you are now aware, your comments regarding Istria and Dalmatia are considered deeply disrespectful to, and have upset, many people in Croatia and Slovenia.”
“In the interests of ensuring the required level of trust as you carry out your responsibilities as President of the European Parliament, who represents both the institution and the members elected to serve in it, the ECR Group calls on you to retract the section of your speech that has caused such offence.”
The letter continues, “I am sure you agree that despite the positive and peaceful Europe that we live in today, it is still important to approach our commemorations of certain events with a necessary degree of sensitivity, particularly given that conflict is so often interpreted in different ways.”
APOLOGY ‘IN PERSON’
Leading S&D MEPs have also strongly condemned the comments made by Tajani, saying his remarks "echo old territorial claims and a nationalist discourse."
They have now urged Tajani to apologise for the statements "in person."
Group leader Udo Bullmann said, "The comments made by President Tajani are deeply concerning and are not acceptable from a President of European Parliament.”
"A person in his position should have the political and historical knowledge and understanding not to make such misleading and nationalistic statements. Rather than fanning the flames of division, he should be working to bring countries and communities back together."
Bullmann added, "It is our duty as Europeans to remember the massacres and violations committed by all countries. President Tajani must apologise for the offence he has caused in person.”
"If President Tajani wants to be a nationalist politician rather than a statesman he should leave his role as President of the European Parliament. Remembrance is vital, but we must also strive to bring people and nations together, not use history to widen our differences.”
“President Tajani must make amends as soon as possible.”
On Friday, this website asked Tajani’s office for a comment but received no reply.