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, though most have largely followed the truce that Abbas agreed with Israel in February, which helped to smooth the Gaza pullout after 38 years of occupation.
The dominant Fatah movement has numerous armed offshoots. Some have carried out suicide attacks in Israel like the Islamic militants. Others have also been heavily involved in arms smuggling, banditry and abductions.
"These groups will be asked to disband, join the security forces or will be dealt with as outlaws that have no right to exist and will be treated accordingly," Husseini said.
All the armed groups hailed Israel's withdrawal from Gaza as a victory for their uprising since peace talks failed in 2000.
"There is no Israeli presence in Gaza, so carrying arms in the streets and having militias isn't justified," Husseini said.
Abbas said this week that he could bring unrest in Gaza under control by the end of the year, but citing fears of civil war he said he would not disarm Hamas - the most powerful faction and one that presents a growing political challenge.
But Abbas has said that after January parliamentary elections, which Hamas plans to contest for the first time, the group would no longer need weapons. Palestinian officials say Abbas wants to get the new parliament to pass a law outlawing the creation of militias.
"After elections Hamas can't mix between being a political party and having armed militias. They have to choose. They are either a militia or a political party," Husseini said.
PA Chairman says will impose order in Gaza immediately In a televised speech Tuesday, Abbas said he would take immediate steps to impose order in chaotic Gaza.
Abbas spoke a day after Israel Defense Forces troops forces pulled out of Gaza. Since the withdrawal, Palestinian security forces have tried to prevent scavenging and looting in abandoned settlements, but have failed in most cases.
Security commanders have said they don't have the manpower to do the job.
Abbas also said that Israel's withdrawal from the Strip was not an end to occupation and that Israel must also withdraw from the West Bank and East Jerusalem.
"The withdrawal of the occupation army and the settlers from the Gaza Strip doesn't mean in any way that occupation has come to an end," he said in the speech broadcast on Palestinian television.
"Today Gaza, tomorrow the West Bank and [East] Jerusalem," he said, referring to the Palestinian demand for a state in all those territories captured in the 1967 Middle East war.
The Palestinian leader is under intense pressure from his people and the international community to stop the growing lawlessness in Gaza, where rival militant groups are jockeying for power. As Abbas spoke, hundreds of Hamas gunmen paraded through the streets of a nearby refugee camp.
In his speech, Abbas promised that "After today, we are not going to hesitate to put an end to all the negative signs and violations of law and order.
"We have one law for everyone and no one is above the law. We are not going to tolerate chaos after today," he said, but did not say how his security forces would improve their performance.
Abbas also outlined ambitious plans for new housing and public works in Gaza.
He said 3,000 housing units would be built in the former settlement of Morag in southern Gaza at a cost of $100 million. Also, he said, 1,210 homes would be built in Rafah, on the Gaza-Egypt border with Saudi funding, and houses wrecked during more than four years of conflict with Israel would be renovated.
Abbas said Palestinians would start building a seaport and repave Gaza's potholed main north-south road.
After the speech, Palestine TV broadcast a new song with the lyrics: "Abu Mazen, the choice of our people, Abu Mazen, the beloved of our people, together we shall overcome all obstacles."
The song, accompanied by video footage showing him in various public appearances, appeared to be part of an attempt to boost Abbas' popularity.
January??!!
He's simply positioning to ask for a check from US taxpayer's pockets to "carry out" such plans.
Arafat continually held this carrot in front of the nose of America, too. It filled his bank accounts quite well.