In a speech to Palestinian police, Abbas pledged to maintain calm during the Israeli withdrawal from the Gaza Strip this summer.
"We have to give them a calm departure," he said, according to a summary of the speech published on Thursday by the Palestinian news agency Wafa.
Abbas has been under pressure from Israel and the United States to rein in Palestinian fighters, who had a relatively free hand under his predecessor, the late Yasir Arafat.
So far, Abbas has preferred to negotiate with the armed groups.
Most of the resistance groups have signed on to an informal ceasefire agreement with Israel.
Drop in violence
While there has been a sharp drop in violence, fighters have fired several rockets at Jewish settlements in Gaza and an Israeli border town in recent days.
Fighters have fired rockets at
Jewish settlements in Gaza
One salvo landed near a large gathering of Israeli demonstrators in a Gaza settlement on Wednesday, lightly wounding one soldier.
Abbas told police officers such violence could not be tolerated.
"Whoever wants to sabotage [the truce] with rocket fire or shooting must be stopped by us even if that requires using force," Abbas said. "There is a national consensus regarding the calm, and whoever departs from this consensus will be struck by an iron fist."
In his speech, Abbas did not single out any specific group.
No one has claimed responsibility for the recent rocket attacks, although a tiny group, the Popular Resistance Committees, has said it opposes the ceasefire and is suspected by Israel of being behind some of the violence.
The biggest groups, Hamas and Islamic Jihad, have largely honoured the truce. Hamas appears to be focusing its efforts on Palestinian legislative elections scheduled in July. Hamas spokesman Mushir al-Masri said on Thursday that Hamas remains committed to a ceasefire but accused Israel of breaking its promises.