The two sides have been bitterly divided since Hamas seized full control of the Gaza Strip in June 2007 after a week of deadly street fighting. The move left the Palestinian president with effective control only in the occupied West Bank.
Osama Hamdan, a senior Hamas representative, told Al Jazeera: "I believe that if he [Arafat] was alive that we may face some different conditions.
"Arafat started the dialogue with Hamas in 2002, hoping to form a new kind of unity, while Abu Mazen [Abbas] worked hard to undermine those negotations at that time.
"In 2003, Abu Mazen participated as the head of Fatah's delegation, and he did his best to undermine the negotiations. So we know Abu Mazen well, and we know he doesn't care about Palestinian unity," Hamdan said.
In a statement issued in Gaza, Hamas also accused the Palestinian police of "working to protect the security of the occupier and not of the Palestinian citizen".
Abbas insisted that his security services were not holding Hamas supporters as "political prisoners" in the West Bank.
Abbas charged Hamas with inventing "false pretexts" for not showing up at the talks with the other Palestinian factions on Tuesday.
"They missed this opportunity and I am talking of the Hamas leadership here."
Abbas also accused Hamas of blocking any commemorative events for Arafat in the Gaza Strip "under the threat of armed force".
Unlike in the West Bank, where thousands of Palestinians turned out to hear the Abbas address, which was carried live on Palestinian television, no events were planned in Gaza.
An organising committee made up of all the main Palestinian factions, except Hamas, accused the group of refusing authorisation to hold any commemoration in the territory.
|While a political resolution evades Palestinians, the Israeli occupation continues [AFP]
But the Hamas-run interior ministry in Gaza said it had received no such request and that it had a responsibility to maintain order.
Last year, a massive memorial rally in Gaza was marred by violence when Hamas police opened fire on the crowd, killing eight people and wounding 130 others.
The Gaza Strip fighting was followed by the ransacking by Hamas supporters of Arafat's former residence in the Gaza Strip.
Hamdan said: "We have two political programmes within the Palestinian situation - the negotiations with Israel, and the resistance to the occupation. We have to reform the PLO [Palestinian Liberation Organisation] and rebuild the Palestinian political structure and then we can talk about the politics.
"Either you are with me, or against me, this is the problem with Abu Mazen," he said.
Nayef Harbiyat, 83, who had travelled to the Ramallah memorial ceremony from Dhahiriya, across the West Bank, bemoaned the loss of the former Palestinian leader.
"With every year that has passed, people realise how much he protected our people. Four years after his death, we are enduring insurmountable divisions."
Maan Ahmad, 16, agreed. "If Arafat were still alive, all of this would never have happened."