Although Mr Fiore, a member of the Third Position cell, was not directly involved in the execution of the bombing, he was convicted for conspiring to carry out an armed attack. He lived in the UK for several years.
"He is absolutely the most extreme person who has ever served in the European Parliament," said Glyn Ford, a Labour MEP. "There are other MEPs who feel strongly about this. We usually put up a cordon sanitaire around the far-Right politicians."
Fiore, who is close friends with Nick Griffen, the chairman of the British National Party, won his seat in Brussels after the resignation of Alessandra Mussolini.
Fiore was part of a far-right coalition, Social Alternative, which won one seat in the parliament in elections in 2005. Alessandra Mussolini had occupied the seat until her resignation in April to serve in the Italian parliament.
Since Mr Fiore was the next highest-ranking member in the coalition, he won the right to become her replacement. Mr Fiore's own party, Forza Nuova, failed to win any seats in the Italian general election last month.
He said his new career as an MEP "could not have got off to a better start".
He took part in a debate in Strasbourg on immigration this week, where he argued for temporary immigrant camps to be dismantled and their residents to be expelled. "I called for a suspension of the Schengen [free movement] treaty so that we can control our borders efficiently," he said.