One of Islamic Jihad's top commanders in the West Bank, Abed al-Khaleem Ezzedine, was arrested during a brief army incursion which was punctuated by gun battles at the western entrance to the city.
Palestinian security sources said around 40 jeeps and tanks had moved into Jenin and surrounded houses as shooting rang out. Two Apache helicopters could be seen circling overhead.
After arresting six Palestinians, the troops left the city. There were no reports of casualties.
Jenin has been the scene of some of the fiercest fighting of the five-year uprising. Some 54 Palestinians and 23 Israeli soldiers were killed during clashes in the city in April 2002.
The operation came less than 24 hours after a suicide bombing claimed by Islamic Jihad which killed five Israelis in the northern town of Hadera. The 21-year-old bomber came from the village of Qabatiya, near Jenin.
Sharon warned that Israel's response to violence would be unstinting in the absence of firm action from the Palestinian Authority.
"Our activity will be wide-ranging and continuous until we have brought about the cessation of terrorism," he said.
"Unfortunately, the Palestinian Authority is not taking any serious steps in, and is not serious about, the struggle against terrorism," he said, calling the attack in Hadera a "severe act".
Palestinian leader Mahmud Abbas condemned the bombing as counter-productive and warned he would not tolerate people taking the law into their own hands.
The five dead were the first Israelis to be killed by Palestinian militants since Israel pulled its troops and settlers out of the Gaza Strip.
The pullout had raised hopes in the international community of a genuine breakthrough in the Middle East peace process but Sharon ruled out a resumption of talks with Abbas unless the Palestinian Authority cracked down on militants.
"If the PA (Palestinian Authority) does not take serious and tangible action against terrorism, there will be no diplomatic progress," he said after talks with Russian Foreign Minister Sergei Lavrov.
The main Palestinian militias are meant to be observing a truce brokered by Abbas in March but Wednesday's attack served as a reminder of its fragility.
Army chief of staff General Dan Halutz was quoted as declaring a "war to the bitter end" against Islamic Jihad after meeting defence chiefs.
Jihad said the attack was to avenge the death of their West Bank military leader who was killed in a gunfight with Israeli troops at the weekend.
"We will not allow the West Bank to become a new Iraq and we will use every means possible in our offensive, including targeted operations," a source closed to Sharon told AFP.
Around a dozen Palestinians, including members of Jihad, were arrested overnight by troops while the air force carried out three air strikes over Gaza without causing casualties.