The Palestinian militant group that governs Gaza, Hamas, has condemned the murder of Italian pro-Palestinian activist Vittorio Arrigoni.
A Hamas spokesman described the killing as "against the humanity... of the Palestinian people".
Mr Arrigoni was found dead hours after being seized on Thursday by a radical group in conflict with Hamas.
Police said he was found hanged in a Gaza City apartment and two people have been arrested.
Mr Arrigoni, 36, was seized by Salafist radicals, an Islamist movement that considers Hamas as too moderate, BBC Gaza correspondent Jon Donnison says.
The Salafists had threatened to execute Mr Arrigoni by 1400 GMT on Friday unless several prisoners, including their leader, Sheikh Abu Walid al-Maqdasi, were released. Sheikh Maqdasi was arrested by Hamas police last month in Gaza City.
In a video posted on YouTube, Mr Arrigoni appeared to have been beaten and his eyes were covered with thick black tape.
A caption on the video read: "The Italian hostage entered our land only to spread corruption." The video called Italy "the infidel state".
It is not clear why Mr Arrigoni was killed before the given deadline, but the Hamas interior ministry said he had died soon after being abducted.
Hamas officials said two people had been arrested and others were being sought, but gave no further details.
Interior ministry spokesman Ehab al-Ghussein said Mr Arrigoni was killed "in an awful way".
Mr Ghussein told reporters that the security forces had been led to the house in Gaza City after a tip-off.
He described the killing as a "heinous crime which has nothing to do with our values, our religion, our customs and traditions", and vowed to hunt down and bring to justice those who were involved.
Hamas spokesman Salama Marouf said the killing went "against the humanity and against the custom and tradition of the Palestinian people".
About 2,000 people in Gaza attended a rally to protest Mr Arrigoni's killing.
In Rome, the Italian foreign ministry expressed "its deep horror over the barbaric murder".
Italian diplomats have been in touch with Israel regarding the transfer of the body from the Gaza Strip, possibly on Sunday, an Israeli official has told the BBC.
His mother said he was a humble man.
"He never hung out with the powerful, he never went to the 'palaces,' if that's what you can call those [headquarters] of Hamas," Egidia Beretta said.
"He had two rooms in this apartment house that overlooked the port," she told Italian TV.
Friends of the activist gathered outside the hospital where his body had been taken on Friday morning.
"He came from across the world, left his country and family and his entire life and came here to break the siege, and we kill him? Why?" asked one of his friends.
Mr Arrigoni was a member of the International Solidarity Movement (ISM) and had been in Gaza for several years.
Huwaida Arraf, a co-founder of the ISM, said he was very well-known in the territory and had a "dynamic, humanitarian personality".
"I even thought that whoever has him is going to see his humanity and just let him go, so when I heard what happened to him I was totally shocked," she told the AFP news agency.
Hamas had been credited with eliminating the threat of kidnapping in Gaza until his abduction.
Mr Arrigoni was the first foreigner kidnapped in Gaza since BBC journalist Alan Johnston was abducted in 2007.
Israeli soldier Gilad Shalit has been held in Gaza since June 2006. He was captured in a raid into Israel by Hamas and other militant groups.