The frictions blocked a rare memorial service for Arafat planned for Gaza, after Hamas said it could not provide security following a series of bomb blasts in the territory.
President Mahmud Abbas, the Fatah leader and Arafat's successor, accused the movement Hamas that controls Gaza of trying "to destroy" efforts to broker national unity.
Hamas hit back, accusing Abbas of uttering "lies, insults and disinformation".
The contrast for the anniversary was striking on the ground in Gaza City and the West Bank city of Ramallah, where Abbas's Palestinian Authority is based.
As a band paid musical tributes, thousands of people waving the yellow flag of Fatah gathered at the Mouqataa compound in Ramallah where Arafat was buried after his death at 75 in 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.
In Gaza City, Arafat's portrait was nowhere to be seen and the stage where a tribute was to have been paid 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 charged that Hamas was behind the Gaza explosions which targeted Fatah leaders.
"Those who caused the explosions in Gaza are the leaders of Hamas -- they are responsible," he said, accusing the rival faction of trying "to sabotage and destroy the Palestinian national project".
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's stronghold.
Following his speech, Abbas was denounced by Hamas as "sectarian and partisan".
"Abbas's speech is a web of lies, insults and disinformation," said Mushir al Masri, a Hamas spokesperson in Gaza.
"What the Palestinian people need is a courageous president."
Fayez Abou Eita, spokesperson for Fatah in Gaza, called for an inquiry into the "terrorist" blasts, which reportedly caused 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.
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The Palestinians needed a Gandhi. but instead got an Arafat. Now their entire political culture is permeated with the ethos of violence that he promoted. The Palestinians will not know peace soon. Even if all the Jews were gone, the Palestinians would soon start strangling each other. Indeed, it is only their mutual hostility toward Israel that keeps them from doing so outright.