Israeli Prime Minister Benjamin Netanyahu is expected to consider Mr Sharansky's proposals, an Israeli official told Reuters news agency.
An unnamed Israeli official speaking to news agency Reuters said the Scud missiles were smuggled into the Hezbollah stronghold of southern Lebanon two months ago.
Anonymous Israeli officials, quoted by AP news agency, said the withdrawal would be completed before US President-elect Barack Obama's inauguration on Tuesday.
"Yasser Arafat has not passed the test of 48 hours of total calm that the prime minister set last Sunday, " said an Israeli official quoted by the French news agency AFP.
"Now we're talking about a permanent easing, " Israeli military spokesman Maj Guy Inbar told the Associated Press news agency.
Official sources told Reuters news agency the force would be deployed once the Israeli withdrawal had been confirmed.
Mr Netanyahu and US envoy George Mitchell released a joint statement after their four-hour meeting at the Park Lane Hotel, saying Israeli officials would meet Mr Mitchell again next week, AFP news agency reported.
An Egyptian security official quoted by AP news agency said the shipment had been made in consultation with Israeli officials who were in Cairo on Thursday.
The Israeli prime minister met officials late on Tuesday to formulate a response, the Associated Press news agency reported.
Israeli security officials said at last 40 rockets fired at southern Israel on Tuesday, reported Reuters news agency.
Iran last week condemned what it also says was an Israeli airstrike on Khartoum, and it called the strike a clear violation of international laws, according to the news agency.
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