The commander, Moussa Alaian, said Abbas ordered the operation after he saw the illegal construction.
"We are a new era now. We must respect the law," Alaian said, indicating the long-ignored laws would now be enforced under the Abbas regime.
Hundreds of heavily armed Palestinian police protected the workers, and large crowds of people came to watch, but there was no resistance.
Egyptian Foreign Minister Ahmed Aboul Gheit told reporters in Cairo that Abbas may visit there next week as part of his efforts to broker a truce. Egypt has worked as a mediator between the Palestinians and Israel in recent years.
US envoy William Burns, a senior State Department official, is to arrive in the region later this week for talks with Israeli and Palestinian leaders on the truce efforts.
In another development, Israel has resumed construction of one of the most sensitive parts of its separation barrier in the West Bank, Israeli media reported Monday.
The 4km section is part of a fence that would surround the settlement of Ariel, deep in the West Bank. Residents of the nearby Palestinian town of Salfit stopped construction for four months by appealing to Israel's Supreme Court.
At first, Israel planned to include Ariel on the "Israeli" side of the barrier, fencing in a significant slice of West Bank land to reach the settlement. Palestinian and international criticism and court cases forced Israel to revise the route, planning instead to build a security fence around the settlement, but it would still enclose Palestinian land.
Israel says it needs the barrier to prevent Palestinian suicide bombers and other attackers from infiltrating. Palestinians charge that the route of the barrier, dipping into the West Bank, amounts to an Israeli land grab.
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