He was addressing thousands of people gathered at a new mausoleum complex in the West Bank city of Ramallah to commemorate Arafat's death.
Abbas also criticised Israel, calling its West Bank separation barrier the "ugly separation apartheid wall".
He said Palestinians remained committed to removing all Israeli settlements and checkpoints in the West Bank.
Abbas pledged to move ahead with peace talks with Israel, a policy condemned by Hamas.
"Peace and security cannot be achieved by aggressive actions and our strategic choice is peace, based on our full adherence to our national rights," he said.
Arafat's tomb, guarded round the clock by members of the presidential guard, has become an obligatory destination for foreign dignitaries who come to the Muqataa compound.
The precise cause of Arafat's death in a Paris hospital in 2004, at the age of 75, remains a mystery.
During his lifetime, Arafat, who died in 2004, guarded against the division that has split the Palestinian territories.
He remains a key figure for Palestinians. Even Hamas, which opposed Arafat's policies during his lifetime, praised the late leader.
"We agreed with president Abu Ammar a lot and we disagreed with him a lot, but in spite of this we consider him a symbol of the Palestinian nation," Fawzi Barhum, a Hamas spokesman, said.
"His memory will endure forever, in every Palestinian boy and girl, in every man regardless of his political affiliations."
Nevertheless, Hamas-run police broke up a number of small demonstrations in the Gaza Strip on Sunday, arresting several young men who were waving the flags of Fatah, witnesses said.
On Saturday, dozens of Palestinian leaders and foreign dignitaries gathered for the opening of the new mausoleum complex at the Muqataa compound.
"The question is will Fatah be strong enough to contain such a powerful 'partner' or will it be just exploited and eroded over time?
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It was at this place that Arafat spent the last years of his life under siege by Israeli forces.
"We inaugurate this everlasting monument in remembrance of the eternal martyr Yasser Arafat who strove in the path of God and his country and his people," Abbas said in a short speech.
The complex measures 11 metres by 11 metres to symbolise the date of Arafat's death.
It includes a 30-metre lighthouse with a laser beacon pointing in the direction of Jerusalem, where Arafat always wished to be buried.
The mausoleum complex will include a mosque and a museum exhibiting his personal effects, items from his office, presents and documents.
Just hours after Abbas's speech on Sunday, the Palestinian side cancelled talks pertaining to the planned Annapolis peace conference.
The team said it was stopped at an Israeli checkpoint, and requested that the preparatory discussions be moved abroad.
"We cannot carry out negotiations like this," Ahmed Qureia, the chief Palestinian negotiator, said after Israeli soldiers blocked his team near Jerusalem.
He and other members of Abbas's team had been scheduled on Sunday night to meet the Israeli team at a location inside Israel.
An aide to Qureia said the negotiators informed Israel they wanted to move the talks to another country but offered no other details.
Mark Regev, a spokesman for Tzipi Livni, the foreign minister who leads the Israeli negotiating team, said: "It shouldn't have happened ... that's not good for peace."
He said Livni called Qureia after the incident, promising an investigation.
Negotiators are struggling to narrow differences over a joint statement to be presented at the Annapolis conference.
Meanwhile, a Palestinian politician has described the Annapolis conference as serving "Israeli and US interests".
In comments aired by Al Jazeera on Sunday, Ramadan Shallah, secretary-general of the Islamic Jihad, said: "Let the whole Arab nation know that there will be no state within the 1967 borders. They have been negotiating the 1967 borders for months.
"Lands will be exchanged, they will take the most important lands in the West Bank and give us few metres in Naqab [Negev] east of Gaza Strip.
"They talk about settlement dismantling; settlements will not be dismantled. They talk about the refugees; the refugees will never return."