Abbas has intensified a crackdown on Hamas after the armed group seized control of Gaza by force in June 2007, leaving him only the West Bank.
Trying to prevent Hamas from taking over the West Bank, Abbas has closed Hamas-linked organisations and arrested hundreds of supporters.
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 on Saturday.
The forces assembled at the city's security headquarters. By mid-morning, several jeeps carrying the new arrivals left the compound and began patrolling the city streets.
Samih Seifi, Hebron's Palestinian security chief, said that he is determined to impose order and would go after criminals as well as fighters.
"We will arrest whoever tries to stop us, and we will not let anyone deter us," Seifi said.
Salam Fayyad, the Palestinian prime minister, said that the deployment was part of a wider campaign to achieve Palestinian statehood.
"Without enforcing law and order, the Palestinians can't live a sustainable life and have a sustainable economy," he said.
The Palestinian forces will not patrol the Israeli-controlled sector where about 650 Jewish settlers live among 30,000 Palestinians.