Around 600 officers are taking up positions in the city, the third in the West bank to be reinforced with forces loyal to Abbas as a maneuver intended to counter the political threat posed by Hamas.
Palestinian security officials said the deployment, which began in the early hours of Saturday, was coordinated with Israel. They added that their forces would remain solely within Palestinian territory, and refrain from patrolling near Jewish areas.
The forces will attempt to cope with Hamas' extensive campaign for political power once Abbas' term comes to an end in January.
The appeal for the deployment of forces was received by Israeli officials and the US security coordinator at the hands of Palestinian Prime Minister Salam Fayyad. The prime minister explained that Hebron was considered the city with the highest risk of being overtaken by Hamas.
Hebron is considered the political fortress of the Islamic Movement. In the most recent parliamentary election, Hamas secured nine seats and is currently running extensive religious and political programs in the area, as well as a number of charities.
Fayyad expressed his government's fears that Hamas' influence would rock the Palestinian Authority's foundations in the city in the wake of the political turmoil expected to ensue once Abbas steps down, and result in a Hamas takeover of the entire West Bank.
In recent months, Abbas has been trying to expand control over the once unruly West Bank, deploying forces first in the cities of Nablus and Jenin, and now in Hebron. Israeli officials have voiced their support for these moves, saying that they helped to impose order in the region.
Several hundred Palestinian police officers are already deployed in Hebron. The new contingent of 585 troops drove into Hebron in jeeps, vans and buses early Saturday.
The forces assembled at the city's security headquarters. By midmorning, several jeeps carrying the new arrivals left the compound and began patrolling the city streets.
Hebron's Palestinian security chief, Samih Seifi, said he's determined to impose order. He said he'd go after criminals as well as militants. "We will arrest whoever tries to stop us, and we will not let anyone deter us," Seifi said.
AP contributed to this article