Abbas, near certain to win a 9 January election to succeed Arafat, made the comments in an interview published on Tuesday, two days after resistance fighters showed their muscle with the deadliest attack on Israeli troops since May.
The US-favoured veteran leader had previously shown his opposition to armed attacks in a four-year-old uprising, but not in such strong terms since Arafat's death on 11 November.
"The uprising should be kept away from arms because it is a legitimate right of the people to express their rejection of the occupation by popular and social means," Abbas told the pan Arab Asharq al-Awsat newspaper.
"The use of arms has been damaging and should end," said Abbas, who took over as head of the Palestine Liberation Organisation after Arafat's death.
Israel ordered more efforts to target resistance fighters after an attack that killed five Israeli troops on Sunday.
Touring the ruins of the army post blown up on the Gaza-Egypt border, Israeli Defence Minister Shaul Mofaz said Israel would keep fighting until the Palestinian Authority began to act against the armed groups.
"We will continue this fight against terror until someone else fights the terror," he said.
Resistance fighters killed five
Israeli troops in Gaza
Troops blew up seven homes in the southern Gaza refugee camp of Khan Yunus after telling residents to leave, Palestinian witnesses said. The army said it destroyed buildings used as cover for firing rockets and mortars at Jewish settlements.
Israeli tanks later rolled up to Gaza City's Shijaia neighbourhood, a stronghold of resistance groups. Gunfire erupted between soldiers and fighters who rushed to the scene.
The latest resistance attacks have also sent a strong message to Abbas and other new Palestinian leaders.
The idea of giving up weapons was dismissed by a spokesman for Hamas militants, who joined with a group from Abbas's own dominant Fatah faction to launch Sunday's attack.
"I believe the consensus of the Palestinian people contradicts these statements," said Sami Abu Zuhri. "The strategies of the Palestinian people should be discussed through a serious and comprehensive dialogue."
Hamas has called for a boycott of the presidential election and a low turnout could damage the credibility of Abbas if it comes to disarming resistance groups.
Israel demands that Palestinian
leaders rein in the resistance
Israel has promised to help ensure that the vote goes smoothly, but that there could be no talks with Palestinian leaders unless they managed to rein in armed factions in a way that Arafat failed to.
Regardless of any negotiations, Israeli Prime Minister Ariel Sharon plans to abandon the Gaza Strip and four of 120 settlements in the West Bank next year under an initiative to "disengage" from the conflict.
Palestinians fear Sharon's real aim is to strengthen Israel's hold on the West Bank in exchange for giving up impoverished Gaza, though Western countries support the plan as a possible step to peace.