Witnesses said fighters of the group had been involved in clashes with Lebanese troops three times since Sunday night.
Munir Maqdah, Fatah's military leader in Lebanon, said the fighting at Ain al-Hilweh had ceased and that the situation was "completely calm".
As the Nahr al-Bared refugee camp, the siege continued into Monday evening, and a bomb exploded in Christian east Beirut, injuring seven bystanders, a senior security official said.
Reports said the bomb exploded on an empty bus close to a commercial centre and a church in the residential and industrial Bouchrieh suburb.
A series of bombings has occurred in and around Beirut since clashes between Fatah al-Islam fighters and Lebanese army forces began on May 20.
In northern Lebanon, troops resumed pounding the Nahr al-Bared refugee camp near Tripoli around 9am local time (0600 GMT) on Monday, targeting fighters from the Fatah al-Islam group holed up inside.
Fifteen days into the seige, Fatah al-Islam has refused to give up its weapons or surrender and is putting up stiff resistance.
Since Friday, the army had conducted an intensive assault on the group's positions at the camp's entrances with the aim of wiping out the group.
John Cookson, Al Jazeera's correspondent at Nahr al-Bared, said the Lebanese army called Monday's attack the "final stages" of its assault on the camp.
Cookson said the attacks "come in waves".
He said: "Secret Lebanese security forces are inside the camp, electronically painting buildings they believe fighters are in. It takes hours, or even a day or so to get the guns lined up."
A 1969 agreement prevents the army from entering Lebanon's 12 Palestinian camps.
The violence, which erupted on May 20, is Lebanon's worst internal fighting since the 1975-1990 civil war. At least 113 people have died and about 25,000 of Nahr al-Bared's 40,000 refugees have fled due to worsening humanitarian conditions.
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The fighting has raised concerns that the violence could spread to more of Lebanon's 12 refugee camps, which hold more than 200,000 Palestinians mostly in conditions of abject poverty.
Mike Hanna, Al Jazeera's correspondent at the camp, said a senior Lebanese army intelligence source informed him that there has been intense communication between Jund al-Sham in the south and Fatah al-Islam in the north, as well as a couple of other armed groups.
The intelligence source said this communication indicates the attacks are co-ordinated and not random.
Fatah's Maqdah, speaking to Al Jazeera from Ain al-Hilweh, said a meeting between members of the mainstream Palestinian factions in the camp - of which Mahmoud Abbas's Fatah is the most powerful - and the Lebanese army aimed to broker a lasting ceasefire and to "re-organise the distribution of checkpoints in the area".
He said: "[The group] Usbat al-Ansar has pledged to control Jund al-Sham members. It is supported by all Palestinian political forces in the camp in order to control the situation.
"An extended meeting will be held with the forces in the camp in order to set the mechanism to avoid other such incidents. We will try to form a field security force where all parties in Ain al-Hilweh refugee camp take part.
Maqdah also said that Fatah was taking security measures inside Ain al-Hilweh to prevent the conflict from expanding.
Source: Al Jazeera and agencies