Abbas described the camp as an “icon of struggle” during his first visit in over a decade to the camp in the northern West Bank city, AFP reported.
Twelve Palestinians and one Israeli soldier were killed last week in the two-day raid on Jenin, the largest in years by Israeli forces.
The raid on the camp, which Israel views as a “terrorism hub”, employed hundreds of troops as well as drone strikes and army bulldozers that tore up streets and damaged scores of houses.
Several top officials of Abbas’s Fatah party, including deputy chairman Mahmoud Aloul, had visited the camp soon after the raid.
On Wednesday, Abbas expressed determination to back Jenin’s reconstruction and security.
He described the camp as an “icon of steadfastness and struggle”, in a short address as crowds of supporters cheered.
“We have come to say that we are one authority, one state, one law,” he said, warning against anyone who “tampers with the unity and security of our people”.
He further vowed to oversee the reconstruction of the camp and the city to restore it “to what it was or even better”.
As he concluded his visit, Abbas laid a wreath on the graves of Palestinians who lost their lives in recent Israeli raids.
A number of Arab countries have announced aid for the camp after last week’s offensive.
The Jenin camp was established in 1953 to house some of those among the 760,000 Palestinians who fled or were expelled from their homes in 1948, the Nakba, or catastrophe, when hundreds of thousands of Palestinians were displaced from their homes following the creation of Israel.
Over time, the camp’s original tents have been replaced by concrete, and it now resembles something closer to a neighbourhood.
The camp, which houses some 18,000 people, was also a hotbed of activity during the second “intifada” or uprising of the early 2000s.
Abbas, 87, last visited Jenin in 2012 but had not toured the camp at the time.