Ehud Olmert, the acting Israeli prime minister, made the statement on Thursday, saying he would use an "iron fist" against Palestinian resistance fighters and al-Qaida.
"I have issued an order to all the security forces of Israel to use special means to confront the buds of terrorist action," Olmert told a news conference in Jerusalem.
"We are systematically intensifying our war.
"No one who fires off a Qassam rocket will have a moment's rest, because we shall seek him out everywhere, track him everywhere, reach him and make sure he is not able to do it."
Qassam rockets are homemade and rarely cause casualties.
"We will use an iron first against any attempt to renew terror activity anywhere," he said. "There are no restraints on security forces to use any means necessary to stop terror attacks."
A day earlier, at a campaign stop in advance of Israeli elections on 28 March, Olmert said Israel would pursue all opportunities for peace.
In recent weeks, Israel has stepped up arrest raids in the West Bank and killed a number of Palestinians in Gaza.
Israeli soldiers where an Israeli
man was shot by a Palestinian
But Israel has denied involvement in the car blast on Wednesday that killed Khalid Dahduh, Islamic Jihad's military commander in Gaza.
On Thursday, an Israeli man was stabbed in the neck at an Israeli factory in northern Jerusalem.
Olmert said: "There are, of course, attempts by terror elements, including international ones, to extend their reach in areas adjacent to us."
Mahmoud Abbas, the Palestinian president, has also said that al-Qaida has infiltrated the Gaza Strip and West Bank, but has given no further details.
Ehud Olmert (L) with Moshe
Katsav, the Israeli president
He was quoted by the Arabic-language Al Hayat newspaper as saying: "We have signs of an al-Qaida presence in the West Bank and Gaza.
"The infiltration of al-Qaida can ruin the whole region."
Israel also says al-Qaida is operating in the Gaza Strip, and that it has arrested a Palestinian allegedly working with the group. Abbas says Palestinian security forces have not captured any al-Qaida operatives.
Osama bin Laden, the leader of al-Qaida, has cited Israel as a target, and the Palestinian cause as one of the reasons for attacks.
Also on Thursday, Israel continued to keep the main cargo crossing in the Gaza Strip closed.
The Karni passage has been closed since an explosion there on 21 February. Extended closures are seen by Palestinians as a collective punishment.
The crossing has been closed for five weeks this year.
Trucks wait at the Karni crossing
On Wednesday, Palestinian officials said they had been told by Israel that the crossing would open on Thursday.
Later Israel said it would not reopen because Palestinians were firing rockets towards Israeli points.
Salim Abu Safiya, director-general of the Palestinian Border Authority, said: "The continued closure is causing humanitarian and economic harm to the Palestinian people, and threatening a real shortage in food supplies."
Palestinian farmers planned to dump hundreds of tons of produce that had nearly spoiled while waiting at the crossing to be exported to Israel and Europe.