Palestinian President Mahmoud Abbas earlier declared a state of emergency and dissolved the government, saying he would form a new Cabinet, replacing the governing coalition in which power has been shared since March by two rival groups.
However, deposed Prime Minister Ismail Haniyeh of Hamas said the government would ignore the decision, which he called "hasty," and blamed Fatah for provoking the Islamists.
Nabil Amr said the new Cabinet would most likely be formed of independent ministers, who have the support of various Palestinian political movements.
"There are currently no negotiations underway with Hamas," Amr said in an interview with the al-Jazeera television station.
More than 30 people died in Thursday's battles, during which Hamas fighters, better armed and more organized than their Fatah opponents, gained a series of decisive victories in Gaza. In the last six days, at least 100 have died in Gaza shootouts.
The Islamist militant group Hamas's string of recent victories in Gaza, where it has taken control of the presidential compound and all key security strongholds, suggests the likelihood that the Palestinian territories will be permanently split into an isolated Hamas-led Islamic state in Gaza and a Fatah-led state in the West Bank.
Some 100,000 people have gathered on Gaza's main square to celebrate the Hamas victory. Crowds of people have been waving the green flags of Hamas and firing automatic weapons into the air.
