Speaking to Israeli radio on Saturday, Amos Gilad, adviser to Defence Minister Shaul Mofaz said: "There is no reason for Israel to grant free passes to VIP Palestinians belonging to an organisation that calls for the destruction of Israel."
Gilad was responding to a question on whether MPs elected to represent the Islamist movement in Gaza would be able to travel to the West Bank, in particular Ram Allah, the headquarters of the Palestinian parliament.
Gilad added that should Hamas's exiled supreme leader Khalid Mishaal try to return to the Palestinian territories he would be "arrested immediately should he enter a zone under Israeli control".
The defence official did not, however, indicate what would happen if Mishaal were to travel to Gaza through the Rafah border crossing with Egypt, which is controlled by Palestinian and Egyptian security forces.
Palestinian newspaper Al-Quds reported on Friday that contacts were underway between Mishaal and the Palestinian administration, as well as the European Union, to "facilitate his return to Gaza" after Hamas's election triumph.
Mishaal lives in Syria and is one of Israel's most-wanted men. He survived an assassination attempt by Mossad agents in Jordan in 1997.
"There is no reason for Israel to grant free passes to VIP Palestinians belonging to an organisation that calls for the destruction of Israel"
Adviser to Israeli Defence Minister Shaul Mofaz
But one senior official in the prime minister's office was more cautious on the question of freedom of movement for Palestinian MPs.
"We will judge on a case by case basis. Those who are directly implicated in terrorism cannot travel. For the others we will see," said the official.
Israel has previously banned Fatah MPs from Gaza whom it believes were implicated in "terrorist activities" from travelling to Ram Allah.
Asked about Mishaal, the source said "any terrorist who moves around does so at his own risk and peril".
Israel's Acting Prime Minister Ehud Olmert has already warned that he will refuse to deal with a Hamas-led Palestinian government.
In the Palestinian territories meanwhile, tensions continued between gangs of Hamas supporters and followers of the Fatah party after a night of armed clashes.
Nine people, five of them security officers, were wounded in shootouts between Fatah and Hamas gunmen in the volatile southern Gaza Strip on Friday, the day after the official election results were published.
Cars set ablaze by rioters in front
of the parliament in Gaza city
The turmoil, which risks intensifying with further demonstrations planned for Saturday, came as the United States threatened to slash aid unless radical Hamas renounces violence.
In Gaza City thousands of Fatah supporters, humiliated by a crushing defeat, called for the party leadership, including Palestinian Authority president Mahmoud Abbas, to resign.
On Saturday, burnt debris littered the streets around the Palestinian parliament building in the city after a night of protests.
Another rally was scheduled for later on Saturday by Fatah supporters opposed to any participation in the new administration.
Hamas leaders, many of them still coming to terms with the scale of their victory, have said they will press Fatah members to join them in a national unity government.