Palestinian security officials said Hamas gunmen opened fire on one of their buildings in Khan Yunus on Friday.
Hamas said its gunmen returned fire after being shot at.
Medics said one Hamas gunman and two security officers were wounded in the incident.
Earlier on Friday, Hamas and Fatah gunmen clashed and three people were wounded.
The violence erupted after Hamas gunmen were angered by a sermon by a Fatah-appointed Muslim preacher during Friday prayers.
The clashes follow Fatah's crushing election defeat by Hamas on Thursday in the historic legislative elections.
Meanwhile, thousands of Fatah supporters took to the streets of Gaza City today, protesting their party's crushing loss and demanding the resignation of the Fatah leadership and its president, Mahmud Abbas.
A mob of young supporters, which included the militant wing of Fatah - the al-Aqsa Martyrs Brigades - marched through the city streets, shooting wildly into the air accusing corrupt elements within Fatah's "old guard" for their party's defeat.
"Fatah is not dead! Fatah is not dead! We will not take part in any Hamas government!"
"Fatah is not dead! Fatah is not dead! We will not take part in any Hamas government!" they shouted as they sped through Gaza City's streets blasting revolutionary music.
Hamas ended Fatah's decades long grip on Palestinian politics when they swept the Palestinian polls in a shocking upset victory.
Many of the supporters also stood in front of President Abbas' Gaza residence, angrily denouncing him as "an Israeli agent" and saying he had three days to resign.
They then swarmed the legislative council, where the Fatah leadership was holding emergency talks to discuss their position after the election results, and directed their anger at symbols of the formerly Fatah-led Palestinian Authority administration.
They burned five vans belonging to the legislative council, and scaled the walls of the building, pulling out air conditioners and wires from its exterior to the cheers of onlookers.
Muhammad Dahalan, the only Fatah leader to win a seat in the district of Khan Yunus and very popular among Fatah's young supporters, came out to calm down the angry mob.
"Anyone who loves this movement should not be attacking it," Dahalan said.
Fatah protesters demanded the
resignation of President Abbas
"Let us not forget this was the first Palestinian movement, founder of the Palestinian struggle, and it will continue to be the first movement - despite attempts by those who conspire against it, conspiracy which led to its defeat," he shouted fervently amidst a sea of yellow flags and rageing bonfires.
Dahalan also urged the crowd to make a forceful showing at a mass Fatah rally set to be held in two days.
"Make your voice heard there," he pleaded, before being whisked away into his private car by his bodyguards against a background of the gunfire.
The mob withdrew, only to march around Gaza City, shouting provocatively to the area's residents, - many of whom stayed indoors - "Do you really want Hamas to rule you?"
Aljazeera Net's correspondent in Gaza, Laila El-Haddad contributed to this report.