Another Israeli minister said all Hamas leaders should be killed with a view to end cross-border rockets being fired into Israel.
Binyamin Ben-Eliezer, the national infrastructure minister, said on Israel Radio on Monday: "I don't distinguish between those who carry out the [rocket] attacks and those who give the orders. I say we have to put them all in the crosshairs."
Asked if Ismail Haniya, the Palestinian prime minister, could be a target, Dichter said: "If Haniya is part of those who give the orders to carry out attacks, that will make him a legitimate target."
Meshaal, who lives in exile in Syria, escaped a Mossad assassination attempt in Amman in 1997.
"Civil war in Gaza is not to anyone's advantage - neither to Israel's nor to the Palestinians"
Ranreshef, Tel Aviv, Israel
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Two Israel agents botched an attempt to poison him then .
"He is not safe anywhere, neither in Damascus or elsewhere," Dichter said. "And he knows this perfectly well."
Haniya also escaped an Israeli attack in Gaza in 2004 that killed Sheikh Ahmed Yassin, the movement's founder and spiritual leader.
"He is linked to the group that has at its heart terrorism against us, but I am not aware if he is among those who directly give the orders" for rocket attacks, Dichter said.
On the ground, Israeli aircraft carried out a series of attacks in the territory on Monday.
At least four Islamic Jihad fighters were killed in an air strike that destroyed their car in east Jabalya in northern Gaza, local residents and medical workers said.
One man was killed in an earlier attack on what Israel called a rocket manufacturing facility and what Palestinians described as a stone mason's shop.
Thousands of Hamas supporters took to the streets of Gaza City and gunmen fired into the air, vowing revenge for the spate of attacks.
The latest offensive came a day after eight Palestinians were killed in an air strike on a Hamas politician's home.
Israel said its air strike on the home of Khalil al-Hayya, a Hamas politician, was not a change of tactics but an attempt to strike gunmen involved in rocket attacks. Hamas said only two of the eight dead were gunmen.
The air strikes also knocked out electricity for about 50,000 people.
Israel's security cabinet decided on Sunday to escalate military action in response to constant rocket attacks from Gaza, which have caused injuries but no deaths and have put political pressure on Ehud Olmert, the Israeli prime minister, to act.