Hamas said a 10,000-strong army, posing on jeeps and camouflage-decorated trucks, spread out across Gaza city on Sunday.
The men carried assault rifles, Qassam rockets and anti-tank missiles as hundreds of thousands of supporters cheered them on.
The demonstration comes one week after Israel completed the evacuation of its forces from the Gaza Strip, ending 38 years of military rule in the impoverished territory, and many Gazans see it as the largest show of force yet by the group.
The demonstration was considered a clear message of defiance to Abbas's calls to disarm Gaza, including his own party's al-Aqsa Martyrs Brigades, under the banner of One Authority, One Weapon.
"We will not allow the state of lawlessness, the disorder of weapons, taking law into one's hands, kidnapping and attacks on government institutions and state land to continue," Abbas said earlier. "No one is above the law."
"We will not allow the state of lawlessness, the disorder of weapons, taking law into one's hands, kidnapping and attacks on government institutions and state land to continue. No one is above the law"
Palestinian Authority leader
The demonstration also the first time commanders of Hamas's armed wing - the Izze-Din-al-Qassam Brigades, long hunted by Israeli drones and helicopter gunships - made a public appearance.
"These are only a small portion of the brigades - spread out on the very same street that our leaders were once assassinated on. If they all came out today, Gaza itself could not fit them," said the one of the younger leaders of the armed wing.
"We are here today to say we shall never lay down our arms. Our arms are our existence," he said.
"We are here to tell the entire world, Israel must leave not just Gaza-but Palestine in its entirety"
Izze-Din-al-Qassam Brigades leader
"It is not a matter of how much it costs us; we will never let up. We are here to tell the entire world, Israel must leave not just Gaza-but Palestine in its entirety.
"Some people say these rockets are child's play. If this is the case, why did the enemy escape from them? We have defeated the army that cannot be defeated. We have crushed the army that cannot be crushed."
Credit for withdrawal
Palestinian factions have been jockeying for power and credit for the Israeli withdrawal in the run-up to Palestinian parliamentary elections in January.
The ability of the Abbas government to come to a swift resolution to the Rafah border crisis, and to re-open the Rafah crossing with Palestinian control, is thought to be a test for his government.
Hamas won the majority of the seats in Gaza's municipal elections this year, and the group's effectiveness at meeting the immediate needs of residents and getting the job done is seen as a challenge to the popularity of the largely mismanaged Palestinian Authority.
Earlier, Israeli Prime Minister Ariel Sharon said that Israel would "make every effort" not to help the Palestinian Authority hold elections in the West Bank if Hamas took part in them.
Hamas leader Mahmoud al-Zahar on Sunday warned Sharon against impeding the Palestinian elections, Aljazeera reported.
Mahmoud al-Zahar (L) says Hamas
opposes Israel's security zones
"Based on Sharon's latest statements about impeding the Palestinian elections and preventing Hamas from participating, we hereby announce that if Sharon impeded the elections process, we have the right to disturb the lives of the Jewish settlers in occupied Palestine by any means viable to us.
"Secondly, Hamas movement opposes any step taken (by Israel) under the pretext of establishing security zones aimed at serving the purposes of the Zionist enemy in any form,'' al-Zahar said.