"President Yasser Arafat has gone but his soul remains with us," Abbas told a 20,000-strong crowd that had gathered in Gaza City's Unknown Soldier square, where Abbas lit a torch to launch festivities marking the 40th anniversary of Fatah, the political movement created by Arafat.
"And as (Arafat) liked to say, the day will come when a Palestinian child hoists the Palestinian flag on Jerusalem's walls, mosques and churches," Abbas said.
He is Fatah's official candidate and favourite to win the January 9 presidential poll to find a successor to Arafat, who died last month.
Abbas is also due to address an election campaign rally during his three-day visit to the impoverished territory, the stronghold for Hamas and Islamic Jihad, the main Islamic radical movements which are boycotting the election.
Fatah dates back its official birth to the first attack it staged against Israel on January 1, 1965, although the group was actually founded five years before in Kuwait.
"It was Yasser Arafat that fired the first bullet" and started our "revolution" said Abbas.
"We will remain faithful to your (Arafat's) legacy until freedom," said Abbas, often interrupted by militants firing salvos in the air and chanting pro-Arafat slogans.