Sharon also told the visiting Egyptian foreign minister Ahmad Mahir on Monday that Israel would halt its attacks against Palestinian resistance activists.
A source close to Sharon said the prime minister had told Mahir that Israel would hold back from major military action if Egyptian efforts to persuade Palestinian resistance factions to lay down their arms succeeded.
"The prime minister made it very clear that he believes in the roadmap for peace," the source told AFP. "It's the only plan that's on the table."
"While Israel is not going to sign any agreement with the terror organisations, he (Sharon) stated that if there's quiet we will respond with quiet. We will refrain from our activity," the source added.
Mahir's visit, his first to Israel in more than two years, comes days after Sharon warned that he would disengage from the peace process within months if the Palestinians did not start meeting their obligations outlined in the "road map".
"I have heard a commitment by Israeli officials to the roadmap, according to which steps have to be taken in parallel by both sides," Egyptian Foreign Minister Ahmad Mahir said after talks with both Sharon and his Israeli counterpart Silvan Shalom in Jerusalem on Monday.
"I told the prime minister (Sharon) that both parties have engagements to fill in a parallel manner in the road map, and he did not disagree."
Reacting to Sharon's statement that he will not meet with "terror" organisations, Hamas said the comment was "nothing new."
"I believe that fits with what we have always said," the group's representative in Lebanon, Usama Hamdan, told Aljazeera.net
Mahir is first Egyptian official to
visit Israel since Intifada began
"There is no possible way to deal with Sharon. He is sealing up the path to any possible solution for the conflict. He (Sharon) worked hard to destroy the last ceasefire", said Hamdan.
"I believe the only possibility for a solution, for peace, is resistance".
The Israeli prime minister, Hamdan added, is destroying not only the peace process, but any hopes for peace.
Hamdan said the visit by Mahir and diplomatic relations between Egypt and Israel, "has not assisted the Palestinians in regaining their rights."
Sharon himself hailed Mahir's visit as an opportunity to not only strengthen ties with Egypt but the Palestinian Authority as well.
"I am certain that the links between Israel and Egypt, the biggest and most important country in the Middle East, are going to be strengthened," Sharon said after talks with Mahir which lasted over an hour.
"I am certain that it will also lead to the strengthening of our relations with the Palestinian Authority and the chances of our reaching an agreement with the Palestinians."
The visit was the first by Mahir in more than two years and a sign of a thaw in relations between the two neighbours.
Egypt, along with Jordan, is one of only two Arab countries to have diplomatic ties with Israel but relations have been strained in recent years with Egypt withdrawing its ambassador after the outbreak of the Al-Aqsa Intifada, or uprising, in September 2000.
Talks also focused on the possibility of an upcoming summit between Sharon and Egyptian President Husni Mubarak, who have not met since the Israeli premier came to power in 2001.
"I think that Egypt can use its influence to put an end to the conflict between Israel and the Arabs," Foreign Minister Shalom said in a joint press conference with Mahir.
"I heard a commitment from Israel to resume negotiations as soon as possible"
Egyptian Foreign Minister
"We want to see the Palestinians back at the negotiations table. We are waiting for a summit between our prime minister and Abu Alaa (Palestinian premier Ahmad Quraya) but unfortunately no date has been set yet. I hope it will take place in the few upcoming days."
The two prime ministers have yet to meet since Quraya came to power in November and an oft-mooted summit has been frequently pushed back.
"I heard a commitment from Israel to resume negotiations as soon as possible," said Mahir.
"I also heard a desire to ease the life of Palestinians and the impression I came out with is a desire to co-operate with us to bring about serious and fruitful negotiations."