He made the recommendation after Israeli troops shot dead a Palestinian teenager in the southern Gaza Strip late on Tuesday when youths charged Israeli positions next to an abandoned Jewish settlement bloc.
Mofaz was speaking at a meeting of ministers presided over by Prime Minister Ariel Sharon which provisionally agreed that the process of recalling Israeli troops would begin next Monday and be finalised by 15 September.
The final date for the historic troop withdrawal, set to draw the curtain on Israel's 38-year occupation of the Palestinian territory, would be agreed to during the main weekly cabinet meeting on Sunday, said an official.
Foreign Minister Silvan Shalom said there was no reason for troops to stay any longer in the Palestinian territory.
"Since the settlements have been evacuated, there is no reason for the army to stay behind any longer," he told public radio.
On Sunday, the cabinet will also rule on the date of handing over control of the so-called Philadelphi corridor to Egyptian forces, who are to man the Gaza-Egypt border in a bid to prevent weapons smuggling.
Earlier on Wednesday, the top-selling Yediot Aharanot newspaper reported that senior Israeli army officers wanted troops pulled out of Gaza immediately after deadly clashes between Palestinians and soldiers.
"Get out of Gaza now" said the front-page headline in Yediot, with a photograph of dozens of Palestinian youths hurling stones at an Israeli tank guarding the Gush Katif bloc of settlements in southern Gaza which was emptied of all its residents more than two weeks ago.
Mofaz: The security of Israeli
citizens is our primary interest
"The danger grows every further day that passes with Israeli troops in the Gaza Strip," said the newspaper, citing senior Israeli soldiers.
Israeli cabinet ministers on Wednesday approved new arrangements at the Gaza-Egypt border, and raised the possibility that it would eventually agree to the movement of Palestinians in and out of Gaza under the supervision of foreign inspectors, without an Israeli presence.
The plan still awaits full approval by the Israeli cabinet next week.
A Palestinian teenager was shot dead on Tuesday after hundreds of stone-throwing youths and Israeli soldiers clashed.
It was the third straight day of violence in the southern Gaza Strip.
Nimr Saduni, 17, and three friends charged into the abandoned Ganeit Tal settlement after two hours of confrontation with the Israeli army and Palestinian security forces.
Saduni and his friends raced past a coil of razor wire on a hill overlooking the Mediterranean, becoming the first Palestinian civilians to enter the Gush Katif settlement bloc after Israel evacuated 8000 settlers from the Gaza Strip last month.
He pumped his fists in the air in triumph and cheered to his fellow stone-throwers below him on the area's sand dunes when a bullet knocked him to the ground, according to an AFP photographer.
Hundreds of teenagers had burned grass on the dunes and forced one Israeli tank to retreat under a hail of debris before the fatal shooting.
In a daily ritual, teenagers from the city of Khan Yunus had flocked to the dunes of the neighbouring Gush Katif settlement bloc, home to Ganeit Tal, with the hopes of being the first to get inside the property's newly found vulnerability.
Palestinian security forces and Israeli soldiers had repelled the stone-throwing teenagers, but on Tuesday, the confrontation, which has gone on for the past week, turned deadly.
Palestinian security men try to
push back stone-throwing youths
Saduni's death raised to 4823 the number of people killed since the Palestinian uprising, or intifada, started in September 2000. The vast majority of the dead have been Palestinian.
Angry youths flooded the Khan Yunus morgue late on Tuesday, pushing adults and medical staff out of the way and kissing their dead friend shrouded in a white sheet.
Later, a homemade rocket was fired from the Gaza Strip on a field in southern Israel, where it exploded without causing any casualties, Israeli public radio reported.
The clashes followed two days of violent protests over unemployment that left 20 wounded in Khan Yunus.
Israel has stripped Gush Katif of many of its watchtowers and anti-blast walls in the countdown to its handover of the settlement bloc to the Palestinians in mid-September..