Although the aide, Rafiq Husseini, provided no timetable, it was the first indication that Abbas would begin to deal with the issue.
Israel and the US have long demanded Abbas disarm resistance groups, especially Hamas and Islamic Jihad, as he is obligated to do under the terms of the internationally backed road map peace plan.
Until now, Abbas has been reluctant to confront the groups, preferring instead to co-opt them.
"The groups within Fatah will be required to disarm and join the security services, or we will have to treat them as if they have violated the law," Husseini was quoted as saying by the Israeli daily, Haaretz.
"There is no longer an Israeli presence in Gaza, so bearing arms in the streets and the existence of militias are not justified. After January, Hamas will no longer need its weapons either," Husseini added.
He was referring to a January parliamentary election, in which Hamas plans to participate.
Abbas plans to begin with the armed wings of Fatah "to show the other groups that the process is serious", Husseini said.