Attacks by hardcore fans of Serie A side Napoli left three more Swedes hurt following a Europa League match Thursday in the southern Italian port city, reports said.
According to the ANSA news agency, the attacks occurred following Napoli's 4-0 win over Swedish side AIK Solna in Group F of Europe's second tier club competition.
Police told the news agency the Swedish supporters were having dinner in Piazza Borsa after 11:00 pm (2100 GMT) when they were approached by a group whose faces were covered.
Two were stabbed in the buttock and leg and the third victim was admitted to hospital for tests. The report did not say whether the third man was also stabbed, but added that the wounds were believed not to be life threatening.
On Thursday police launched a hunt for what they called "pseudo fans" of Napoli who stabbed two Swedes and the owner of the pizzeria where they were eating after an ambush late on Wednesday night.
Reports said the pizzeria owner was injured while trying to defend the Swedish fans against "a group armed with baseball bats and knives".
Luigi de Magistritis, the mayor of Naples, said Friday it was time to stop labelling the perpetrators "fans" of the club.
"We should call them criminals, not fans, because that's what they are," said De Magistritis. "Napoli can go far in both the Europa League and Serie A but we as fans and as a city still have a long way to go.
"I urge all fans, whether in organised groups or not, to keep well away from these criminals."
Naples police superintendent Luigi Merolla called the first attacks late on Wednesday night an isolated incident.
But he also likened them to similar incidents in the town in 2010 when hardcore "ultras" left three supporters of Liverpool in hospital with stab wounds.
Police were expected on Friday to step up their hunt for the criminals.