Khalil al-Hayya, the head of Hamas's faction in parliament, told 100,000 of the movement's supporters at a noisy rally in Gaza City: "What a war Mahmoud Abbas you are launching, first against God, and then against Hamas."
Ismail Haniya, the prime minister and leader of Hamas, was more conciliatory at the rally, appealing for "national unity", but stopping short of explicitly calling for calm as he had during previous spikes in internal fighting.
At least 32 Hamas supporters in the West Bank city of Ramallah were wounded by gunfire from Abbas's forces, hospital officials said. Several were in critical condition.
Unity government
Tensions were at their highest in a decade and followed months of failed talks to form a unity government between the ruling Hamas Islamist faction and Abbas's once-dominant Fatah.
Hayya said Hamas would not agree to holding an early election or a referendum on the issue, a move that Abbas could announce in a speech planned for Saturday in an attempt to break the political deadlock.
Hayya did not say what Hamas would do if Abbas made such a dramatic announcement.
The violence broke out after Hamas, which controls the Palestinian Authority, accused a Fatah strongman and Abbas's presidential guard of trying to kill Haniya outside the Rafah border crossing with Egypt.