Hamas hit back, accusing Abbas of uttering "lies, insults and disinformation".
Arafat founded the Fatah movement in the late 1950s and since his death, the recurring refrain can be heard across the West Bank to Gaza: "There would never have been any Palestinian division under Arafat."
Palestinians are unanimous in their belief that their iconic national leader would not have allowed the quasi civil war between Fatah and Hamas in 2007 which saw the Islamist movement ousting their rivals from Gaza and the establishment of two separate administrations.
But today, the divide remains stark, despite efforts to bridge the gap by means of a spring reconciliation agreement.
In the West Bank city of Ramallah, a band paid musical tributes as thousands waved the yellow flag of Fatah at the Muqataa presidential compound where Arafat was buried after dying, aged 75, at a hospital near Paris on November 11, 2004.
"The hour of freedom and independence has arrived," read a giant banner on the stage where Abbas gave a speech.
But in Gaza City, Arafat's portrait was nowhere to be seen and the stage where the tribute was to have taken place bore the marks of an explosion last Friday.
"We were hoping this anniversary would mark the end of Palestinian divisions and show national unity, with Hamas standing alongside Fatah in paying tribute," said Suheila Barbah, a young woman in Gaza City.
Arafat was "the personification of national unity," said Refaat Hajaj, a Gazan in his 30s. "They have deprived us of this anniversary."
In his speech for the anniversary, Abbas accused Hamas of responsibility for the 10 blasts which targeted Fatah homes and property on Friday.
"Those who caused the explosions in Gaza are the leaders of Hamas -- they are responsible," he said, accusing the movement of trying "to sabotage and destroy the Palestinian national project".
- Arafat's legacy -
Earlier this year, the two movements signed a reconciliation agreement aimed at ending seven years of bitter and sometimes bloody rivalry which saw the West Bank and Gaza ruled by separate administrations.
The deal led to the creation of a national consensus government which took office in Ramallah but has yet to fully exert its powers in Gaza.
Hamas denounced Abbas as "sectarian and partisan".
"Abbas's speech is a web of lies, insults and disinformation," said Hamas spokesman Mushir al-Masri. "What the Palestinian people need is a courageous president."
Fayez Abu Eita, Fatah's Gaza spokesman, called for an inquiry into the "terrorist" blasts, which caused damage but no casualties.
Abbas also reaffirmed his plans to submit a draft resolution to the UN Security Council this month calling for an end to Israel's occupation of the Palestinian territories by November 2016.
He promised that the Palestinians, who won the UN rank of observer state in 2012, would apply to join a host of international organisations if the resolution was blocked by a US veto.
In a letter to mark the anniversary, Marwan Barghuti, a prominent jailed Palestinian, said that "choosing global and armed resistance" was being "faithful to Arafat's legacy, to his ideas and his principles for which tens of thousands died as martyrs."
He also remarked on the still unexplained circumstances of Arafat's death, saying his "assassination" was the result of "an official Israeli-American decision".
Two years ago, Swiss experts who examined the personal effects of the veteran Palestinian leader reported finding "abnormal" levels of polonium, an extremely radioactive toxin, fuelling the widespread Palestinian belief that he was poisoned by Israel.
Israel has repeatedly denied any role in Arafat's death.