Rehavam Zeevi will be buried in Jerusalem on Thursday
In a first retaliatory step, Israel has banned Mr Arafat from using the international airport in Gaza.
In apparently related incident, a suicide bomber blew himself up near Israel's border with the Gaza Strip on Wednesday evening, injuring two Israeli soldiers.
The Popular Front for the Liberation of Palestine (PFLP) said it carried out both the killing of Zeevi and the suicide bombing near kibbutz Nahal Oz.
It is the first time the secular leftist PFLP has said it carried out a suicide bombing. The technique is more commonly associated with militant Islamic groups.
Memorial session
Israel's inner security cabinet met on Wednesday night to discuss further responses amid intense international diplomatic pressure to show restraint.
Mr Sharon earlier told a special memorial session of parliament: "I hold Arafat fully responsible, as he set the terrorism in motion, even though he knew very well what the consequences would be."
Aides to Mr Arafat have denied responsibility for the killing and say the Palestinian leader has ordered the arrest of the people who carried it out.
Separately, Israel's internal security agency, the Shin Bet - which seldom makes public statements - has said it will "work night and day to find the murderers of Israeli minister Rehavam Zeevi and bring them to justice".
US President George W Bush has condemned the killing "in the strongest terms", White House spokesman Ari Fleischer said.
"This despicable act is further evidence of the need to fight terrorism," Mr Fleischer said in a statement released during a stop in California as Mr Bush headed to China for a summit.
An unnamed senior US official told Reuters that the killing must not be allowed to derail the shaky Israeli-Palestinian ceasefire agreed on 26 September.
The official added that it was "clear" that Zeevi killing had been "carried out in defiance of Palestinian leaders, who have called for a ceasefire".
Hotel shooting
Zeevi, a 75-year-old former general, was the head of the right-wing National Union Party and resigned from the government on Monday in protest at Israel's military pull-out from Hebron.
He was shot in a Jerusalem hotel on the day that his resignation from cabinet was due to come into effect.
The PFLP said it carried out the assassination in revenge for the killing of its leader, Abu Ali Mustafa, by Israeli forces in August.
Israel Radio reported that Mr Arafat phoned Foreign Minister Shimon Peres to express his condolences and promised to make every effort to find the killers.
No bodyguards
Zeevi had been having breakfast in the dining-room of Jerusalem's Hyatt hotel with his wife before he made his way up to their room on the eighth floor, police said.
Once there he was approached by two gunmen who shot him at close range, including twice in the head.
Zeevi had no bodyguards with him at the time and the gunmen were able to escape.
When his wife followed him up to their room 10 minutes later she found him lying in a critical condition in front of the door, police said.
An American tourist, David Hocking, who was also staying in the hotel, ran into the corridor after hearing Zeevi's wife screaming.
Mr Hocking said that he had not heard any shots fired and the police are investigating whether a silencer was used.