Sharon told the UN General Assembly on Thursday that "now it is the Palestinians' turn to prove their desire for peace," after Israel withdrew from the Gaza Strip following a 38-year occupation.
"The most important test the Palestinian leadership will face is in fulfilling their commitments to put an end to terror and its infrastructure (and) to eliminate the anarchic regime of armed gangs," he said.
"Until they do so, Israel will know how to defend itself from the horrors of terrorism," Sharon warned.
On Friday planning minister Ghassan Khatib criticised Sharon's call for Palestinians to now prove their desire for peace as lacking credibility because of Israeli plans to expand settlements and build its separation barrier in the West Bank.
"This was a public-relations speech to exploit the withdrawal from Gaza and to realise diplomatic gains, no more. It has no credibility as he goes on with his policy to build the barrier and the settlements," Khatib said.
Sharon insisted Israel was committed to the internationally drafted "road map" peace plan, which paves the way to the creation of a Palestinian state.
He said the success of the Gaza pullout "opens a window of opportunity for advancing towards peace in accordance with the road map".
"They (the Palestinians) are also entitled to freedom and to a national sovereign existence in a state of their own," he said.
Palestinians want Israel to begin
dismantling the West Bank wall
Khatib said the Palestinians had wanted Sharon to "announce Israeli readiness to go back to bilateral negotiation on the basis of the implementation of the road map".
Late on Thursday, those sentiments were also echoed by chief Palestinian negotiator Saeb Erakat.
"The Palestinian Authority calls on the Israeli government to relaunch the peace process with a view to a permanent solution that establishes frontiers as well as the status of Jerusalem and of Palestinian refugees," Erakat said.
The road map plan, which calls for an end to all Israeli settlement activity, has made next to no progress since its launch in 2003.