At least four people were wounded in the first fighting between the groups - two police, one member of the Hamas force and a gunman from Mr Abbas's Fatah movement.
Intense clashes sent terrified residents fleeing from the night-time streets of Gaza City, where tension has soared amid fears that confrontation between the forces could lead to civil war.
US Secretary of State Condoleezza Rice said the emergence of rival security forces was a "dangerous situation" that she hoped Mr Abbas could resolve.
Police station surrounded
Members of the Hamas force, mostly bearded young militants who fought Israel in an uprising for years, surrounded the main police station in Gaza City and traded fire with those inside.
"It began with the two sides shouting at each other and it developed into a gunfight," said one policeman who had brought a wounded comrade to hospital.
The 3,000-strong Hamas-backed force, formed under the authority of Interior Minister Saeed Seyam, was deployed in a challenge to the authority of Mr Abbas, whose Fatah movement was defeated by Hamas in elections in January.
In response, Mr Abbas ordered the deployment of a Fatah-loyal police unit. The decision marked the latest step in a deepening power struggle between Mr Abbas and Mr Haniyeh, whose Hamas movement took power in March.
The rival deployments followed growing insecurity in Gaza, with at least five rival gunmen killed this month. "It seems that the civil war has begun," said one medic, who did not want to give his name as gunfire echoed.
The Fatah gunman was shot in front of the hospital as he pleaded that he was nothing to do with the clashes. Gunmen with weapons cocked peered warily around street corners in the densely populated seaside city.
Abbas loyalists have far more forces under their control than Hamas, but many of them are poorly equipped.
Isolation campaign
Tensions have been exacerbated by a financial crisis since Hamas took control. Western donors have cut funding to the aid-dependent Palestinian Authority to try to force Hamas to recognise Israel, renounce violence and accept past peace agreements.
Hamas is formally committed to destroying the Jewish state, though it has largely followed a truce for more than a year. Mr Abbas is seeking to revive negotiations for a Palestinian state in Gaza and the occupied West Bank.
The United States, leading the campaign to isolate Hamas, has put its faith in Ms Abbas, who was elected in 2005 on a platform of peace making.
Condoleezza Rice said in Washington that she hoped the situation of rival security forces could be resolved.
"We obviously believe that president Abbas, who we believe has the confidence of the Palestinian people, should be able to exercise his responsibilities as president of the country," she said.
"All Palestinian parties ought to respect the need of the Palestinian people to have a secure environment and not to have a situation in which there is violence in the streets. The Palestinian leadership has every obligation to get control of it."