About 1,000 men marched through the streets of Gaza on Thursday, chanting: "We are the authority. We salute Abu Mazen."
Abu Mazen is the nom de guerre of Mahmoud Abbas, the Palestinian president and head of the Fatah movement.
Their street protest was in response to Wednesday's deployment by Hamas of 3,000-fighters, mostly members of its military wing, the Izz al-Din al-Qassam Brigades, armed with assault rifles, grenades and missiles.
The policemen ran through the streets and conducted drills near Hamas patrols. The men were unarmed, but were followed by commanders in Jeeps, their weapons raised in the air.
They chanted: "Jerusalem, the president, the homeland," and clapped and whistled.
General Sulaiman Hilles, commander of the Palestinian security forces in the West Bank and Gaza, said the forces were deployed to send a message that "the Palestinian police are the only side that can maintain law and order".
However, the lines are not clearly drawn; some police officers also back Hamas.
Several hundred officers met Ismail Haniya, the prime minister, on Thursday and professed their loyalty to the Hamas-led government.
"The Palestinian police are the only side that can maintain law and order"
General Suleiman Hilles, commander of Palestinian security forces in the West Bank and Gaza
Haniya told them that the new unit was formed legally and that it would work alongside the security forces.
Saeb Erikat, an Abbas adviser, said that the president had asked the government to take the new unit off the streets immediately.
However, Haniya said the unit was legal and suggested it would not be disbanded.
The unprecedented Hamas-Fatah friction, including deadly drive-by ambushes against two Hamas gunmen in Gaza earlier in the week, came amid new efforts to explore a possible revival of peace talks with Israel.
Erikat said that Abbas was to hold talks on Sunday with Tzipi Livni, the Israeli foreign minister, the first high-level meeting since Hamas came to power in March.
Israel has said it will not resume negotiations, even with Abbas, unless Hamas softens its anti-Israel views.
Some police have professed their
loyalty to Hamas government
Without a Hamas about-turn by the end of the year, Israel plans to unilaterally begin drawing borders with the Palestinians under a plan by Ehud Olmert, the Israeli prime minister.
Olmert is expected to make his first trip to Washington as prime minister next week, and is expected to come under US pressure to try to negotiate a deal with Abbas.
Israel could present the Abbas-Livni meeting to its Washington hosts as a goodwill gesture.