"The withdrawal of the [Israeli] army and settlers from the Gaza Strip does not signal the end of the occupation", Abbas said in a televised address on Tuesday after the last Israeli soldiers left Gaza early on Monday.
"The occupation will not end until the objectives of the peace process, namely the creation of an independent Palestinian state with Jerusalem as its capital in the territories which were occupied in 1967, have been met," he said.
"The conflict will not end until these objectives have been achieved."
Warning to fighters
At the same time, he delivered a clear warning to any armed group seeking to challenge his authority that everybody must obey the law.
The fighters claim credit for the Israeli pullout.
"We will not allow anybody to destroy this achievement under any justification. This is the future of our sons. Today there is no room for personal agendas," he said.
"We will not allow the armed chaos and people taking the law into their own hands or kidnappings or attacking public property.
Abbas warned fighter groups to
obey the law
"The principle that unites us is that we have one authority, one law and one legal weapon," he added, referring to the arms of the Palestinian security services.
Israel has also demanded disarmament as a precondition for statehood talks.
The president's chief of staff, Rafiq Husseini said Abbas planned to start by disarming the small armed groups within his own Fatah movement before moving on to bigger, better armed and more disciplined organisations such as Hamas and Islamic Jihad.
Small groups first
"President Abbas will act against the small groups, especially those groups that claim to be part of Fatah," Husseini said.
"The president will start with his own house first to show other groups that he is serious," he added.
Husseini did not say exactly when any disarmament would start or whether force would be used to get groups to comply.
So far, Abbas has preferred to use persuasion over force.
The factions have consistently rejected any suggestion that they would disarm, although most have largely followed the truce that Abbas agreed to with Israel in February, which helped to pave the way for the Gaza pullout after 38 years of occupation.