Reports say at least five Palestinians - including a two-year-old boy - have been hurt by machine-gun fire as soldiers make house-to-house searches for suspected militants.
Meanwhile, the Israeli army said troops had started pulling out of another West Bank town of Hebron.
The incursion into Jenin follows a suicide car bombing on Monday that killed 14 Israelis and came as a US Middle East envoy held talks with leading Palestinians.
'Capital of terror'
The militant Palestinian group Islamic Jihad admitted responsibility for the suicide attack near Hadera and the two bombers came from Jenin.
Israel's Defence Minister Binyamin Ben-Eliezer said the town and its refugee camp had become a "capital of terror".
Troops pulled out of Jenin only last week and a curfew was lifted after months of occupation, but Mr Ben-Eliezer said: "When I speak of men and women suicide bombers, this is where they come from."
He added: "We don't have a choice but to go in and try to clean up what it's possible to clean up."
Houses taken over
The Israeli army said the Jenin operation - dubbed Vanguard - was the biggest military offensive since an incursion into the West Bank city of Nablus in August.
Eyewitnesses said that troops had taken over about 50 houses in the battle-scarred city which they were using as look-out posts.
Palestinian leader Yasser Arafat said the incursion was "a continuation of the crimes committed by Israeli soldiers and settlers against our people and our children".
He said the Israelis were undermining any hopes for a peace process, which was being discussed by US Assistant Secretary of State William Burns.
Significantly, Mr Burns has no plans to meet Mr Arafat whom both the US and Israelis consider an obstacle to peace.
Peace plan briefing
He has met other Palestinian officials on his current trip and on Friday he presented the new peace plans separately to Palestinian legislator Hanan Ashrawi and rights activist Mustafa Barghouti.
The plan - supported by the "quartet" of the US, United Nations, European Union and Russia, envisages a three-stage process to Palestinian statehood by 2005.
Mr Barghouti said Mr Burns told him the Americans were committed to building a Palestinian state.
Ms Ashrawi echoed previous reservations about the plan expressed by both Palestinians and Israelis.
"I think it needs quite of a bit of work, but it's a draft," she said, adding that the plan needs to hold Israel to its commitments, including a full withdrawal from Palestinian areas.
Israel says the peace plan lacks security guarantees while the Palestinians say it needs firm timetables.