Two Palestinian security men were fatally wounded in the exchange of fire between the armed men and bodyguards shielding Abbas, also known as Abu Mazin.
Abbas, 69, was uninjured, security officials said.
Speaking to reporters later, Abbas said that emotions were running high after the death of Yasir Arafat.
He denied any remarks were made against him. "No slogans were chanted against me. It was not an assassination attempt," he said.
Former Palestinian security minister Muhammad Dahlan, who served under Mahmud Abbas when he was prime minister last year, also denied that the shooting inside the mourning tent in Gaza this evening was an assassination bid.
Dahlan told Aljazeera, "To report that it was an attempt to assassinate Abu Mazin is not true."
Abbas was hustled into the tent
by guards when shooting began
Aljazeera footage showed a chaotic scene as heavy gunfire erupted inside the tent.
Abbas was on a visit to accept condolences for the Palestinian president, who died on Thursday.
The chaos erupted after masked armed men from Arafat's faction-ridden Fatah movement shouting "No to Abu Mazin", a critic of violence, walked by him as he stood outside the mourning tent and began firing shots into the air.
Members of Arafat's president guard hustled Abbas into the tent and threw him to the ground for his safety as shooting intensified.