French news agency quotes an unnamed Israeli defence ministry spokesman as saying that Defence Minister Binyamin Ben Eliezer gave the order.
Earlier on Tuesday, Palestinian leader Yasser Arafat issued another strongly-worded order to his military commanders to secure a ceasefire on all fronts.
The statement called for armed Palestinians to exercise maximum restraint even when they come under fire.
Washington has been pressing for some progress in the Israeli-Palestinian conflict in order to make it easier to involve moderate Arab states in any coalition to fight international terrorism.
Mr Arafat's comments on the ceasefire were immediately welcomed by Israeli Foreign Minister Shimon Peres.
"This is an important declaration with positive elements, including
his global commitment for peace and with explicit instructions for a ceasefire,"
Mr Peres said in a statement.
In a series of interviews on Monday, Israeli Prime Minister Ariel Sharon insisted that ceasefire talks with the Palestinians were not in Israel's national interest, whatever Washington's hopes for building an international coalition.
Mr Sharon blocked long planned talks between Mr Arafat and Israeli
Foreign Minister Shimon Peres on Sunday.
Correspondents say American officials were not best pleased by Mr Sharon's description of Yasser Arafat as "our Osama Bin Laden".
It appears that Washington is encouraging Palestinians to join in the war against terrorism declared by the US after the attacks on Washington and New York.
In his statement on Tuesday, Mr Arafat said he had told US officials that he was ready "to put all our capabilities at their disposal, and to be part of the international alliance to put an end to terrorism against innocent and unarmed civilians".
Show of solidarity
Mr Arafat played host to a range Arab and foreign ambassadors, the US and British consuls, the UN envoy Terje Roed-Larsen, and EU envoy Miguel Moratinos at his official residence in Gaza.
Our correspondent says the meetings were a show of solidarity by the Palestinian leader with the international community and some indication that the international community remains willing to place its faith in Mr Arafat.
After issuing his statement, Mr Arafat was asked whether his ceasefire orders extended to the militant Islamic groups Hamas and Islamic Jihad.
He answered that the ceasefire was a matter for all Palestinians.
Violence continues
Also on Tuesday, an area of Gaza City came under Israeli tank fire. Reports say there were no injuries but several houses were damaged.
The Israeli army said it was responding to a Palestinian mortar attack.
On the West Bank, in Nablus, a Palestinian was shot dead when he failed to respond to orders to halt as his tractor approached an Israeli military post.
In Hebron, a Palestinian taxi driver's body was found at the scene of intense overnight gun battles between Palestinian gunmen and Israeli soldiers.