Israel has yet to respond to the declaration, although a state official said earlier that there was no such agreement but that efforts would be made to maintain the calm – if Hamas chose to do so.
The Color Red alert system was activated at around 9:30 pm, and the rocket is believed to have hit an open area without causing any injuries or damage.
The Home Front Command on Sunday evening lifted the limitations imposed on gatherings and activities in educational institutions in the threatened communities.
The Palestinian factions said they had decided to give a ceasefire a chance "for the Palestinian people" and "in order to give them room to breathe."
In a statement issued Sunday evening, the factions said that although they agreed to a truce, "the time will come when the occupation pays a heavy price for its foolishness. The occupation understands nothing but the language of force."
The factions stressed that the deal was signed with extra caution as Israel "is treacherous and violates agreements."
Netanyahu was briefed on the anti-missile system by one of the soldiers operating it, and said that "this is a great achievement, thanks to its operators."
The prime minister stressed that "we can't defend every house, facility and site in this country," adding that the cabinet instructed the IDF to work to stop the rocket fire and restore calm.
He added, "I hope this will be Hamas' intention as well. If this will be Hamas' intention, calm will be restored. If it reinforces its attacks, our response against Hamas will be much tougher."
Some 20 Qassam rockets and mortar shells exploded within Israel on Sunday, a dramatic drop compared to the weekend fire. There were no reports of injuries or damage in all incidents.
Meanwhile, the Defense Ministry released a video of the Iron Dome missile defense system intercepting a rocket launched from the Gaza Strip.
The images, which were captured by a camera that was attached to the battery, show in slow motion the moment in which the interceptor Tamir missile hits the rocket and destroys it midair.
Arab League Chief Amr Moussa said Sunday that the organization would ask the United Nations Security Council to impose a no-fly zone over Gaza, which Israel has pounded with air strikes in response to rocket fire.
Condemning what it called Israel's "brutal" aggression in Gaza, a gathering of the Arab League's permanent delegates chaired by Oman called on the UN to convene its Security Council.
An Israeli government official in Jerusalem, who declined to be named, dismissed the call and said the Arab League should first ensure Gaza militants halt attacks on Israel.
"If the Arab League wants a no-fly zone in Gaza is it also talking about ground-to-ground missiles that are fired from Gaza on Israeli cities? About missiles fired at school buses? About mortar shells fired at farms?" the official said.
"If the Arab League wants Israeli military aircraft to stop flying over the Gaza Strip then it should first ensure there is no reason for them to be there to protect Israeli citizens."
Elior Levy, Attila Somfalvi, Shmulik Hadad and Reuters contributed to this report
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