The images appear to show Hamas fighters laughing as one seems to say "This is for Abu Mazen and the next one is for the Preventative Security."
Watch footage of the alleged assassination attempt
Abu Mazen is the name by which the Palestinian president is also known.
The tape was released on the same day that Abbas agreed to meet Ehud Olmert, the Israeli prime minister, for the first time since Hamas took control of Gaza.
Jamal Nazzah, a Fatah spokesman, told Al Jazeera: "This is not the first time Hamas has tried to kill Abbas. In our view this was part of a plan to make a coup against the Palestinian Authority."
Atef Adwan, a Hamas MP, responded: "If Hamas had wanted to kill president Abbas then we would have done this years ago.
"We don't want to do this as president Abbas represents the legality of the Palestinian system."
Red Sea summit
Abbas and Olmert will meet at the Egyptian Red Sea resort of Sharm el-Sheikh on Monday, officials said.
Hosni Mubarak, the Egyptian president, and Jordan's King Abdullah will meet Abbas there on Sunday before the four-way summit.
Before the meeting, Israel's cabinet is expected to agree on Sunday to release hundreds of millions of dollars of Palestinian tax revenues collected by Israel.
They have been withheld for the past 15 months since the Hamas movement formed a Palestinian government after winning a parliamentary election.
For his part, Abbas is issuing orders to disband armed groups - both from Hamas and the al-Aqsa Martyrs Brigade - which is nominally loyal to his own Fatah faction.
'Project of darkness'
On Wednesday, Abbas said Hamas replaced the "national project" with "its project of darkness", attacking the symbols of government in Gaza
, including the house of the late leader Yasser Arafat.
The televised speech was Abbas's toughest since he fired the Hamas-led cabinet and replaced it with his own team of Fatah supporters and experts over the weekend.
"Our main goal is to prevent sedition from spreading to the West Bank, ... to prevent violations by any party, and to deal [with everyone] equally, based on law," Abbas said.
He accused Hamas of trying to set up its own state in Gaza alone, a step he said would scuttle Palestinian hopes for independence.
He said he had tried to prevent the conflict through "continuous dialogue". Instead, "we are seeing assassination of leaders of Palestinian security and Fatah in Gaza".
"It's a fight between the national project and this small kingdom they want to establish in Gaza, the kingdom of Gaza, between those who are using assassination and killing to achieve their goals, and those who are using the rules of law."
Sami Abu Zuhri, a Hamas spokesman, rejected Abbas's statements.
"What he said was disgusting and not appropriate for the Palestinian president," the Hamas official said.
"The president has harmed himself with his words."
|Thousands of Hamas supporters demonstrated |
against Abbas on Wednesday[AFP]
Ayman Taha, another Hamas official, told AFP that the speech was "a joke, contains a lot of contradictory statements, is misleading and a pack of lies".
Not long after Abbas's speech, Hamas backers on the streets of Gaza city denounced him as an agent of Israel and the US.
Thousands of people chanted anti-Abbas slogans and rallied in support of the Hamas movement. They also burned US and Israeli flags, and pictures of Abbas and Condoleezza Rice, the US secretary of state.
Source: Al Jazeera and agencies