Two police officers have been wounded in a gun battle between Palestinian factions in Gaza City.
Palestinian police loyal to Fatah have been parading in Gaza
Police supporting the mainstream Fatah party said they had been attacked by a militant-led force set up by the new Hamas government - a claim it denies.
The clash came after the two rival security forces paraded through the streets in a show of strength.
Rivalry between the Fatah and Hamas has intensified since Hamas' victory in parliamentary elections in January.
Hamas has rejected calls by Palestinian leader Mahmoud Abbas to withdraw its force, first deployed in Gaza on Wednesday.
Palestinian PM Ismail Haniya, from Hamas, said the new force was legal and would provide support for the police and the Palestinian people.
The latest fighting erupted near Gaza City's parliament building just after midnight, in the early hours of Friday morning, the Associated Press news agency reports.
Officials told the agency the two policemen had been shot in the legs and the injuries were not serious.
BBC correspondent Alan Johnston says the origins of the clash are unclear but it comes as no surprise, given present tensions.
Recent clashes between armed members of the two groups have left five people dead in Gaza.
The new Hamas force was first deployed on Wednesday
Earlier on Thursday, thousands of policemen from the existing Palestinian force, loyal to Fatah, marched through Gaza's streets, chanting slogans in support of Mr Abbas.
Reports say they whistled and clapped as they passed gunmen from the new force, deployed a day earlier by Hamas.
US Secretary of State Condoleezza Rice warned on Thursday that the rivalry had created a "very tense" situation - and said all security forces should be brought under the control of Mr Abbas.
"President Abbas, who we believe has the confidence of the Palestinian people, should be able to exercise his responsibilities," Ms Rice said.
Her comment echoed earlier remarks by Saeb Erekat, a senior aide to the Palestinian leader.
Mr Erekat told the BBC Hamas should disband its force.
"I think the situation is a pressure-cooker situation," he said. "We don't want anything that may endanger the situation or push it from bad to worse."
Hamas has formed the new force in defiance of a veto by Mr Abbas.
The unit is led by Jamal Abu Samhadana, a militant who is wanted by Israel.
It includes some members of Hamas' military wing as well as others from existing security forces.
Its stated role is to ensure the safety of citizens and protect property amid a wave of instability and violence.
Hamas officials announced the creation of the new force in April, after Mr Abbas appointed one of his supporters to lead the most important of the three branches of the security services that report to the interior ministry.
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